ODE No. 1165

\[ (a+x) y'(x)+x^2 y''(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0724572 (sec), leaf count = 26

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

\[\left \{\left \{y(x)\to \frac {c_2 (a+x)}{a^2}+c_1 x e^{a/x}\right \}\right \}\]

✓ Maple : cpu = 0.023 (sec), leaf count = 19

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

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