partial differential equation of order two

[AnyHelpIsAppreciated]

Hi,
english is not my native language so i hope the translation is correct, thanks in advance if you help!

(see photo if its unclear)
Problem: Calculate the partial differential equation d/dx ( f(x,y)-2*x*d/dy(f(x,y)) = y with variable switch { u=a*x^2 } and {v=x}

After doing the derivation and simplifying i got to the follow equation: f'(u)*(2*a*v-2)+f'(v)+f''(uu)*2*a*v+f''(uv)-2u = y
I was wondering what to do next, how do i simplify this and solve the equation?

 

[Deleted member 4993]

Hi,
english is not my native language so i hope the translation is correct, thanks in advance if you help!

(see photo if its unclear)
Problem: Calculate the partial differential equation d/dx ( f(x,y)-2*x*d/dy(f(x,y)) = y with variable switch { u=a*x^2 } and {v=x}

After doing the derivation and simplifying i got to the follow equation: f'(u)*(2*a*v-2)+f'(v)+f''(uu)*2*a*v+f''(uv)-2u = y
I was wondering what to do next, how do i simplify this and solve the equation?

That does not look correct!

Neither 'u' (=a*x^2) nor 'v' (= x) is function of 'y'. However, Right-Hand-Side of the derived expression, you have a 'y'. That would be very unusual.

Can you please show us - how you derived that expression?