Solve the differential equation? dy/dx= (x^2+y)^2 - 2x?

[scorpion]

[h=1]Hi.
Any one have an idea how to solve this question?
Solve the differential equation? dy/dx= (x^2+y)^2 - 2x?[/h]dy/dx= (x^2+y)^2 - 2x? Hint let u =x^2+y

Thanks.

 

[Deleted member 4993]

Hi.
Any one have an idea how to solve this question?
Solve the differential equation? dy/dx= (x^2+y)^2 - 2x?

dy/dx= (x^2+y)^2 - 2x? Hint let u =x^2+y

Thanks.

You were given a hint - what did you do with it?

y = u - x^2

dy/dx = du/dx - 2x

then

du/dx - 2x = (x^2 + y)^2 - 2x

continue.....

 

[scorpion]

Hi.
I thought i will have to do something like this :

u =x^2+y

then

du/dx = 2x dy/dx

the substitute into equation

 

[scorpion]

You were given a hint - what did you do with it?

y = u - x^2

dy/dx = du/dx - 2x

then

du/dx - 2x = (x^2 + y)^2 - 2x

continue.....

Hi.

I thought i needed to solve it like this :

u =y+ x^2

Then

du/dx=2x dy/dx--------(dy/dx)=(1/2x)(du/dx)

Then I substitute (dy/dx)=(1/2x)(du/dx) into original equation.

Thanks.

 

[Deleted member 4993]

Hi.

I thought i needed to solve it like this :

u =y+ x^2

Then

du/dx=2x dy/dx--------(dy/dx)=(1/2x)(du/dx)

Then I substitute (dy/dx)=(1/2x)(du/dx) into original equation. ... OKay - do it!

Thanks.

What did you get after substitution.

 

[Deleted member 4993]

Hi.

I thought i needed to solve it like this :

u =y+ x^2

Then

du/dx=2x + dy/dx--------(dy/dx)=(du/dx) - 2x ........ corrected

Then I substitute (dy/dx) = (du/dx) - 2x into original equation. ........ corrected

Thanks.

Correction of your work