Given, (6x4y1)dy= (3x2y1) dx ️ dy/dx=(3x2y1)/(6x4y1)(i) In which, a=3 b= (2) & a1= 6 & b1= (4) {Since, We know that, If dy/dx= (axbyc)/a1xb1yTiger Algebra gives you not only the answers, but also the complete step by step solution for your Quadratic Equations 2x^3ydx(x^4y^4)dy=0 so that you can understand betterSimplify (2xy)(3x^2y) Expand using the FOIL Method Tap for more steps Apply the distributive property Apply the distributive property Apply the distributive property Simplify terms Tap for more steps Simplify each term Tap for more steps Rewrite using
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2x/y^3dx+y^2-3x^2/y^4dy=0-Substituting y 3 = t so the equation will be 1 3 d t d x ( 2 x 2 − 1) t 3 x ( 1 − x 2) = a x 3 3 x ( 1 − x 2) after this the integrating factor is 1 x 1 − x 2 But I am unable to solve it forward calculus ordinarydifferentialequations Share Visit https//wwwmathmunicom/ for thousands of IIT JEE and Class XII videos, and additional problems for practice All free Over 1 million lessons deliver
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So, using the quotient rule d dx ( u v) = vdu dx −u dv dx v2 the second derivative is given by d2y dx2 = (3y)( d dx2x) − (2x)( d dx3y) (3y)2 ∴ d2y dx2 = 6y −(2x)( dy dx d dy3y) 9y2 ∴ d2y dx2 = 6y −(2x)(3dy dx) 9y2 ∴ d2y dx2 = 6y −6xdy dx 9y2 ∴ d2y dx2 = 6y −6x(2x 3y) 9y2 ∴ d2y dx2 = 6y − 4x2 y 9y2Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Find dy/dx 3x^22xyy^2=2 3x2 2xy y2 = 2 3 x 2 2 x y y 2 = 2 Differentiate both sides of the equation d dx (3x2 2xy y2) = d dx (2) d d x ( 3 x 2 2 x y y 2) = d d x ( 2) Differentiate the left side of the equation Tap for more steps By the Sum Rule, the derivative of 3 x 2 2 x y y 2 3 x 2 2 x y y 2 with respect to x
For any parabola, Ax 2 BxC, the x coordinate of the vertex is given by B/(2A) In our case the x coordinate is Plugging into the parabola formula for x we can calculate the y coordinate y = * 075 * 075 30 * 075 40 or y = 2875 Parabola, Graphing Vertex and XIntercepts Root plot for y = 2x 23x4 The question is basically to find out the solution of the differential equation $$(2x^23y^27)xdx(3x^22y^28)ydy=0$$ Since the given differential equation is non homogeneous I tried to find out the point of intersection of $2x^23y^27=0$ and $3x^22y^28=0$I got the point of intersection and then I tried to shift the coordinate system to thatFactor 3x^22xyy^2 Factor by grouping Tap for more steps For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is Tap for more steps Reorder terms Reorder and Factor out of Rewrite as plus Apply the distributive property
Problem Solve the following differential equations first finding an integrating factor $$ ( 5xy 4y^2 1 ) \, dx ( x^2 2xy ) \, dy = 0 $$ Answer I have no idea how to find an integrating factorMove all terms containing d to the left, all other terms to the right Factor out the Greatest Common Factor (GCF), 'd' d(3x 7xy 2x 2 6y 4y 2) = 0 Subproblem 1 Set the factor 'd' equal to zero and attempt to solve Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right Simplifying d = 0It is homogeneous equation
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#int 2( y 1) d y = int 3x ^ { 2} 4x 2 d x # #y^2 2y = x^3 2x^2 2x C # using the IV #(1)^2 2(1) = C implies C = 3 # #implies y^2 2y ( x^3 2x^2 2x 3) = 0 # From the Quadratic Formula #y = (2 pm sqrt(4 4 ( x^3 2x^2 2x 3)))/(2)# #y = 1 pm sqrt(x^3 2x^2 2x 4)# Checking the IV againThis is a simple homogeneous (because of the '= 0') second order (because of the d^2y/dx^2) differential equation First, form the auxiliary equation (aka the characteristic equatioDirectrix y = −13 4 y = 13 4 Select a few x x values, and plug them into the equation to find the corresponding y y values The x x values should be selected around the vertex Tap for more steps Replace the variable x x with 0 0 in the expression f ( 0) = 2 ( 0) 2 − 3 ⋅ 0 − 2 f ( 0) = 2 ( 0) 2 3 ⋅ 0 2 Simplify the result
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3x y = 2 replace x by 1 and the equation becomes 3(1) y = 2 do the multiplication of 3 times 1 and the equation reduces to 3 y = 2 Get rid of the 3 on the left side by subtracting 3 from both sides of the equation to reach the solution y = 2 3 = 1 So the solution to this problem is x = 1 and yTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Solve `(xy1)dx (2x 2y3)dy=0`Theory Roots of a product 61 A product of several terms equals zero When a product of two or more terms equals zero, then at least one of the terms must be zero We shall now solve each term = 0 separately In other words, we are going to solve as many equations as there are terms in the product Any solution of term = 0 solves product
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However we can perform a transformation to remove the constants from the linear numerator and denominator Consider the simultaneous equations {x 2y −3 = 0 2x y −3 = 0 ⇒ {x = 1 y = 1 As a result we perform two linear transformations Let {u = x −1 v = y −1 ⇔ {x = u 1 y = v 1 ⇒ ⎧⎨⎩ dx du = 1 dy dv = 1 And if weFree exact differential equations calculator solve exact differential equations stepbystepSubproblem 2 Set the factor ' (3x 4xy x 2 1y 4y 2 )' equal to zero and attempt to solve Simplifying 3x 4xy x 2 1y 4y 2 = 0 Solving 3x 4xy x 2 1y 4y 2 = 0 Move all terms containing d to the left, all other terms to the right Add '3x' to each side of the equation 3x 4xy x 2 1y 3x 4y 2 = 0 3x Reorder
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Move all terms containing d to the left, all other terms to the right Factor out the Greatest Common Factor (GCF), 'dy' dy(xy 2 3x 2 3x 3 y 2) = 0 Subproblem 1 Set the factor 'dy' equal to zero and attempt to solve Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the rightHow do I solve the differential equation d^2y/dx^23(dy/dx)2y=0?3dx^{3}12y^{2}dx^{2}4dy^{4}=0 3 d x 3 1 2 y 2 d x 2 4 d y 4 = 0 Combine all terms containing d Combine all terms containing d Solution to the differential equation (2x^2xy2y^2)dx(3x^22xy)dy=0 (x^33xy^2)dx(3x^2yy^3)dy=0 (x 3
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Find dy/dx x^2y3x^24=0 Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps By the Sum Rule, the derivative of with respect to is Evaluate Tap for more steps Differentiate using the Product Rule which states that is where and This is how to do it To make an inexact differential equation into an exacttype, multiply an integrating factor I(x, y) to the entire differential equation Our integrating factor would be xpyq Solve for p and q to make it exact y(2 − 3xy)dx − xdy = 0 (2y − 3xy2)dx − xdy = 0 xpyq((2y − 3xy2)dx − xdy = 0) (2xpyq 1 − 3xp 1yqExtended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music
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Follow Ebenezer's logic as far as (x^6 2x^4y^2 x^2y^4 y^6)dy = (x^5y 2x^3y^3 xy^5)dx which I rewrite as (x⁶ 2x⁴y² x²y⁴ y⁶)dy = (x⁵y 2x³y³ xy⁵)dx Let y = xz So dy = x dz z dx Then (x⁶ 2x⁶z² x⁶z⁴ x⁶z⁶)(x dz z dx) = (x⁶主要是凑微分， 2x/y^3dx (y^23x^2)/y^4dy =d (x^2)/y^3 (1/y^2)dy (3x^2/y^4)dy =d (x^2/y^3)d (1/y) =d (x^2/y^31/y) =0 则x^2/y^31/y=C (C是常数） 1年前 1 can you please explain how to to find dy/dx for the function x^2 y Y^2 x = 2 asked in CALCULUS by mathgirl Apprentice differentiation;
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1 Answer1 Active Oldest Votes 2 (x2y2 − 1)dy 2xy3dx = 0 Let X = x2 which leads to (Xy2 − 1)dy y3dX = 0 y3dX dy y2X = 1 Considering the unknown function X(y), this is a linear ODE It is easy to solve it The general solution is X(y) = c y − 1 y2 y2X − cy 1 = 0 y = c ± √c2 − 4X 2X y = c ± √c2 − 4x2 2x2 ShareSteps for Solving Linear Equation ( 2 x y ^ { 2 } 3 ) d x ( 2 x ^ { 2 } y 4 ) d y = 0 ( 2 x y 2 − 3) d x ( 2 x 2 y 4) d y = 0 Use the distributive property to multiply 2xy^ {2}3 by d Use the distributive property to multiply 2 x y 2 − 3 by d \left (2xy^ {2}d3d\right)x\left (2x^ {2}y4\right)dy=0 Grouping like terms, #dy/dx = 3y 1/2x 3# In general, we want a differential equation of this type to follow the form #dy/dx p(x)y = q(x)# #dy/dx 3y = 1/2x 3#
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帮忙解一道全微分方程的题 2x/y^3dx(y^23x^2)/y^4dy=0 请将步骤写的详细一些,我找不到怎么错的 扫码下载作业帮 拍照搜题一拍即得How do I solve (X*22xyy*2) dx (y*22xyx*2) dy=0?Steps for Solving Linear Equation ( 2 y ^ { 2 } x 3 ) d x ( 2 y x ^ { 2 } 4 ) d y = 0 (2y2x − 3)dx (2yx2 4)dy = 0 Use the distributive property to multiply 2y^ {2}x3 by d Use the distributive property to multiply 2y2x−3 by d \left (2y^ {2}xd3d\right)x\left (2yx^ {2}4\right)dy=0
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Solution for (2xy)dx(y^23x^2)dy=0 equation Simplifying (2xy) * dx (y 2 3x 2) * dy = 0 Remove parenthesis around (2xy) 2xy * dx (y 2 3x 2) * dy = 0 Multiply xy * dx 2dx 2 y (y 2 3x 2) * dy = 0 Reorder the terms 2dx 2 y (3x 2 y 2) * dy = 0 Reorder the terms for easier multiplication 2dx 2 y dy(3x 2 y 2) = 0 2dx 2 y (3x 2 * dy y 2 * dy) = 0 2dx 2 y (3dx 2 y dy 3) = 0 Combine like terms 2dx 2 y 3dx 2 y = 1dx 2 y 1dx 2 y dy 3 = 0 Solving 1dx 2 ySolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreIn this math video lesson on Higher Order Derivatives, I find the third derivative of y=3x^52x with respect to x #derivatives #higherorderderivatives #calc
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Plot 3x^22xyy^2=1 Natural Language;The equation is now solved \left (2xd5yd3d\right)x\left (2x4y6\right)dy=0 Use the distributive property to multiply 2x5y3 by d 2dx^ {2}5ydx3dx\left (2x4y6\right)dy=0 Use the distributive property to multiply 2xd5yd3d by x 2dx^ {2}5ydx3dx\left (2xd4yd6d\right)y=0Move all terms containing d to the left, all other terms to the right Factor out the Greatest Common Factor (GCF), 'dx' dx(4y 2 3x) = 0 Subproblem 1 Set the factor 'dx' equal to zero and attempt to solve Simplifying dx = 0 Solving dx = 0 Move all terms
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