Solving PDE: Finding a General Solution

[y_fotsing]

I am trying to solve this partial differential equation

$$\frac{\partial^2 \rho (x)}{\partial x^2} + (ax+b)\frac{\partial \rho (x)}{\partial x} + c \rho (x) = const$$

a, b and c are constant value.
Could someone give me a general solution of this king of ode?
Thanks in advance.

 

[fzero]

You might try using the Laplace transform http://en.wikipedia.org/wiki/Laplace_transform_applied_to_differential_equations