ODE No. 1253

\[ x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0 \]

✓ Mathematica : cpu = 0.0162399 (sec), leaf count = 34

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

\[\left \{\left \{y(x)\to \frac {\sqrt {2} c_1}{x}+\frac {c_2 \log (2 x+2)}{\sqrt {2} x}\right \}\right \}\]

✓ Maple : cpu = 0.009 (sec), leaf count = 16

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

\[y \left (x \right ) = \frac {c_{1} \ln \left (1+x \right )+c_{2}}{x}\]