How do you find the general solution of differential equations?

[Fritz]

I really don't understand the concept of differential equations! I'm confused about how you would go about solving them.

if (x^2).dy/dx = y^2,

integral(y^2)dy = integral(x^2)

1/3y^3 = 1/3x^3 + A

^ What have I done wrong here?


I don't get the whole thing where you separate the variables etc.

Am I right in saying that integral(dy/dx)dx = y?

Please can someone help me understand all of this? I understand basic differentiation and integration.

[HallsofIvy]

I'm glad to hear that you understand differentiation and integration but your problem here is algebra!

If x2(dy/dx)= y2, then

dy/dx= y2/x2 and

(dy/dx)/x2= 1/x2 or

y-2(dy/dx)= x-2. Now

y-2dy= x-2dx. (Note the NEGATIVE powers.)

Integrating both sides,

-y-1= -x-1+ C

[Fritz]

I do understand that now, thanks.