2.1181   ODE No. 1181

\[ x^2 y''(x)+(3 x-1) y'(x)+y(x)=0 \] Mathematica : cpu = 0.0344571 (sec), leaf count = 37

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

\[\left \{\left \{y(x)\to \frac {c_1 e^{-1/x}}{x}-\frac {c_2 e^{-1/x} \operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )}{x}\right \}\right \}\] Maple : cpu = 0.035 (sec), leaf count = 25

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

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