wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Solve the differential equation: x(xy)dy+y2dx=0

Open in App
Solution

Given differential equation is x(xy)dy+y2dx=0

dydx=y2x(xy)

Putting y=vx

v+xdvdx=v2x2x(xux)

v+xdvdx=v2x2x2(1u)

xdvdx=v2(1v)v

=xdvdx=vv1

1xdx=v1vdv

On integrating both sides

logx=vlogv+c

Putting v=yx

logy=yx+c

On e both sides

elogy=ey/x+c

y=cey/x

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Methods of Solving First Order, First Degree Differential Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon