differential equation question

[rcd111]

hey guys wondering if you could help....

this is a differential equation in which you have to sub in v=y/x to the equation in order to work it out the general solution. hope you can help me on it.

dy/dx = y/x + (2x^2cos(x^2))/y

find the general solution

[Mattywoo2]

I'll assume you mean cos²(x) in there, as cos(x²) is not intergrable as we know it.

dy/dx = y/x + (2x² cos²(x))/y

Let y = xv, then dy/dx = x dv/dx + v

Substitute these expressions into our DE to eliminate y.

x dv/dx + v = v + (2x² cos²(x))/xv

x dv/dx = (2x cos²(x))/v

dv/dx = (2cos²(x))/v

This is a first order separable DE. Can you do the rest?

Hint: 2cos²(x) = 1 + cos(2x)



All the best, Matt

[rcd111]

cheers managed to get an answer from there thanks very much!