Derivatives of a higher order - Satisfying the equation

[K.QMUL]

Homework Statement

Show that y= xe^x satisfies

A(d²y)/dx² + B(dy/dx) + Cy = 0

for suitably chosen values of the constants A, B, and C.

Homework Equations

Y=xe^x

The Attempt at a Solution

Please see the attachment. I get to a point where I need to find the value of A, B and C but cannot as I'm dealing with x² terms.

Help would be much appreciated.

 

[Office_Shredder]

You calculated dv/dx wrong.

 

[K.QMUL]

Could you explain Where I went wrong?

 

[K.QMUL]

Oh, I see the mistake, Thanks