ODE No. 1141

\[ (3 a+b x) y'(x)+a x y''(x)+3 b y(x)=0 \] Mathematica : cpu = 0.116849 (sec), leaf count = 79

DSolve[3*b*y[x] + (3*a + b*x)*Derivative[1][y][x] + a*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-\frac {b x}{a}}-\frac {c_2 e^{-\frac {b x}{a}} \left (a^2 e^{\frac {b x}{a}}-b^2 x^2 \text {Ei}\left (\frac {b x}{a}\right )+a b x e^{\frac {b x}{a}}\right )}{2 a^2 x^2}\right \}\right \}\] Maple : cpu = 0.042 (sec), leaf count = 55

dsolve(a*x*diff(diff(y(x),x),x)+(b*x+3*a)*diff(y(x),x)+3*b*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {\Ei \left (1, -\frac {b x}{a}\right ) {\mathrm e}^{-\frac {b x}{a}} c_{2} b^{2} x^{2}+c_{1} {\mathrm e}^{-\frac {b x}{a}} x^{2}+a c_{2} \left (b x +a \right )}{x^{2}}\]