Differential equaion with boundary conditions

[follow_the_sun]

Hello, friends,
I try to solve the differential equation with boundary conditions
[MATH] \begin{cases} x\cdot a\dfrac{d^2y}{dx^2}+a\cdot\dfrac{dy}{dx}+c\cdot y\cdot x=d\cdot x - e\\ y(x_0)=y_0 \\ y'(0)=0 \end{cases} [/MATH]How can I solve this system?

 

[Romsek]

looking at what Mathematica returns... not easily.

[MATH]y(x) = \frac{1}{4} \left(-\frac{2 \pi e x Y_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \, _1F_2\left(\frac{1}{2};1,\frac{3}{2};-\frac{c x^2}{4 a}\right)}{a}+\frac{\pi d x^2 \, _0\tilde{F}_1\left(;2;-\frac{c x^2}{4 a}\right) Y_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a}-\frac{4 d J_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c J_0\left(\frac{\sqrt{c} \text{x0}}{\sqrt{a}}\right)}-\frac{2 \pi d x J_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) Y_1\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{\pi ^2 e x \pmb{H}_{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) J_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) Y_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a}+\frac{\pi ^2 e x \pmb{H}_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) J_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) Y_1\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a}+\frac{4 \text{y0} J_0\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{J_0\left(\frac{\sqrt{c} \text{x0}}{\sqrt{a}}\right)}\right)[/MATH]