o 0/1 points I Previous Answers LarCalc10 6.3.076 My Notes Ask Your Teacher Solv

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o 0/1 points I Previous Answers LarCalc10 6.3.076 My Notes Ask Your Teacher Solve the homogeneous differential equation in terms of x and y. form M(x, y) this form by the method of separation of variables, use the substit A homogeneous differential equation is an equation of the dx + N(x, y) dy = 0, where M and N are homogeneous functions of the same degree. To solve an equation of Need Help? Road ITaik to a Tuter Submit Answer Save Progress Submit Assignment Save Assignment Progress Home My Assignments Extension Requesf 41907-2017 Advanced Instructional Systems, Inc. All rights reserved.

Explanation / Answer

We have given equation (x3+y3)dx-xy2dy=0

(x3+y3)dx=xy2dy

dy/dx =(x3+y3)/(xy2)

dy/dx =(x3)/(xy2)+(y3)/(xy2)

dy/dx =(x2)/(y2)+y/x

substitute y=vx,dy/dx=v+x(dv/dx) and v=y/x

v+x(dv/dx) =(1/v)2+v since x/y=1/v and v=y/x

x(dv/dx) =(1/v)2

(dv/dx) =(1/v2)*(1/x)

separate the variable

v2dv=dx/x

integrating both sides

v3/3=ln(x)+C

v3=3*ln(x)+C

v=[3*ln(x)+C]1/3

substitute back v=y/x

y/x=[3*ln(x)+C]1/3

y=x*[3*ln(x)+C]1/3

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