2.1242   ODE No. 1242

\[ \left (x^2-1\right ) y''(x)+\left (x-x^2\right ) y(x)-(3 x+1) y'(x)=0 \]

✓ Mathematica : cpu = 0.420824 (sec), leaf count = 68

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

\[\left \{\left \{y(x)\to c_1 e^{-x} (x+1)^2-c_2 e^{-x-2} \left (x^2 (-\text {Ei}(2 (x+1)))-2 x \text {Ei}(2 (x+1))-\text {Ei}(2 (x+1))+2 e^{2 x+2}\right )\right \}\right \}\]

✓ Maple : cpu = 0.085 (sec), leaf count = 41

dsolve((x^2-1)*diff(diff(y(x),x),x)-(3*x+1)*diff(y(x),x)-(x^2-x)*y(x)=0,y(x))
 

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