ODE
\[ (a+x) y'(x)+x^2 y''(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.254315 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2 (a+x)}{a^2}+c_1 x e^{a/x}\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 19
\[\left [y \left (x \right ) = \left (a +x \right ) \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{\frac {a}{x}} x\right ]\] Mathematica raw input
DSolve[-y[x] + (a + x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(a/x)*x*C[1] + ((a + x)*C[2])/a^2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+(a+x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = (a+x)*_C1+_C2*exp(a/x)*x]