Easy differential equation question

[rock.freak667]

Homework Statement

Obtain the ordinary differential equations whose solution is
i)y=Ae^2x+Bxe^2x
ii)y=mx+ h/m where h is a constant and m is to be eliminated

Homework Equations

The Attempt at a Solution

For the first one it is simply:
y''-4y'+4y=0

For the second one it is just y''=0?

 

[gabbagabbahey]

Not quite, y''=0 has a general solution y=Ax+B with no restrictions on A or B...you want an ODE that gives a more restrictive solution, one where A=m and B=(a constant)/m...so you need a more restrictive ODE...try a first order ODE instead of a second order one.

 

[rock.freak667]

But if I use a 1st order ODE, I won't eliminate the constant m