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