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 = 0.0333029 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {c_1 (a+x)-\frac {c_2 x e^{a/x}}{a^2}}{a+1}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) = \left ( a+x \right ) {\it \_C1}+{\it \_C2}\,{{\rm e}^{{\frac {a}{x}}}}x \right \} \] Mathematica raw input
DSolve[-y[x] + (a + x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((a + x)*C[1] - (E^(a/x)*x*C[2])/a^2)/(1 + a)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+(a+x)*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (a+x)*_C1+_C2*exp(1/x*a)*x