Which Part of My Differential Equation Solution Is Wrong?

[hotjohn]

Homework Statement

i am given dy/dx +( y/x ) = x(y^3) , using transformation of function = y=v/x , but my ans is wrong , which part of my working is wrong ?

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

i am given dy/dx +( y/x ) = x(y^3) , using transformation of function = y=v/x , but my ans is wrong , which part of my working is wrong ?

Homework Equations

The Attempt at a Solution

It's very difficult to read your images.

Can you type them out?

 

[hotjohn]

It's very difficult to read your images.

Can you type them out?

Which part of the working that you can't read?

 

[SammyS]

Which part of the working that you can't read?

None of it is easy to read.

I did zoom in & struggled through.

When you substitute back in for v (to eliminate v) what did you plug in ?From now on, please try to follow the forum rules more closely.

 

[hotjohn]

None of it is easy to read.

I did zoom in & struggled through.

When you substitute back in for v (to eliminate v) what did you plug in ?From now on, please try to follow the forum rules more closely.

ok , thanks for pointing out my mistake

 

[HomogenousCow]

This is actually a really cool problem, it's a "Reverse" homogeneous equation.

 

[Sahil Kukreja]

There is another method to solve this Differential equation is by converting it to exact form

multiply the whole equation by xdx

=> $xdy + ydx = x^2y^3dx$
now multiply and divide by x on RHS

$xdy + ydx = (xy)^3(dx/x)$

now using xdy + ydx = d(xy)

$\frac {d(xy)} {(xy)^3} = \frac {dx} {x}$

$\int \frac {d(xy)} {(xy)^3} = \int \frac {dx} {x}$

now it is easily integrable