ODE No. 1304

\[ x^3 y''(x)+x y'(x)+(-2 x-3) y(x)=0 \] Mathematica : cpu = 0.0491631 (sec), leaf count = 50

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

\[\left \{\left \{y(x)\to \frac {c_2 \left (e^{\frac {1}{x}} \text {Ei}\left (-\frac {1}{x}\right )+2 x^3-x^2+x\right )}{6 x}+\frac {c_1 e^{\frac {1}{x}}}{x}\right \}\right \}\] Maple : cpu = 0.031 (sec), leaf count = 38

dsolve(x^3*diff(diff(y(x),x),x)+x*diff(y(x),x)-(2*x+3)*y(x)=0,y(x))
 

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