General solution to the differential equation

[ZedCar]

Homework Statement

Find the general solution to the differential equation:

(d2y/dx2) - 2(dy/dx) + y = 0

Homework Equations

The Attempt at a Solution

Is my solution correct?

(dy/dx) - 2 + (y^2)/2 + C1 = 0

y - 2y + (y^3)/6 + C1 + C2 = 0

-y + (y^3)/6 + C1 + C2 = 0

y = (y^3)/6 + C1 + C2

Thank you

 

[rock.freak667]

You have a 2nd order ODE with constant coefficients. You need to firstly solve the auxiliary equation formed when you substitute the trial solution y = e^rx.

 

[epenguin]

Homework Statement

Find the general solution to the differential equation:

(d2y/dx2) - 2(dy/dx) + y = 0

I think you ought to be able to recognise that as

$$(\frac{d}{dx} -1)^2 y =0$$