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

## 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 ?

## The Attempt at a Solution

#### Attachments

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SammyS
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## 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 ?

## The Attempt at a Solution

Can you type them out?

Can you type them out?
Which part of the working that you can't read?

SammyS
Staff Emeritus
Homework Helper
Gold Member
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.

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

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

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

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