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

  • Thread starter hotjohn
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  • #1
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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 ?

Homework Equations




The Attempt at a Solution

 

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  • #2
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 ?

Homework Equations




The Attempt at a Solution

It's very difficult to read your images.

Can you type them out?
 
  • #3
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It's very difficult to read your images.

Can you type them out?
Which part of the working that you can't read?
 
  • #4
SammyS
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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.
 
  • #5
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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
 
  • #6
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This is actually a really cool problem, it's a "Reverse" homogeneous equation.
 
  • #7
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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