# Dy/dx +( y/x ) = x(y^3)

1. Feb 14, 2016

### hotjohn

1. The problem statement, all variables and given/known data
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 ?

2. Relevant equations

3. The attempt at a solution

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2. Feb 14, 2016

### SammyS

Staff Emeritus

Can you type them out?

3. Feb 14, 2016

### hotjohn

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

4. Feb 14, 2016

### SammyS

Staff Emeritus
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.

5. Feb 15, 2016

### hotjohn

ok , thanks for pointing out my mistake

6. Feb 15, 2016

### HomogenousCow

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

7. May 13, 2016

### 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

Last edited: May 13, 2016