ODE
\[ x^2 y''(x)-3 x y'(x)-5 y(x)=x^2 \log (x) \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0196094 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_1 x^5+\frac {c_2}{x}-\frac {1}{9} x^2 \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={x}^{5}{\it \_C2}+{\frac {{\it \_C1}}{x}}-{\frac {{x}^{2}\ln \left ( x \right ) }{9}} \right \} \] Mathematica raw input
DSolve[-5*y[x] - 3*x*y'[x] + x^2*y''[x] == x^2*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> x^5*C[1] + C[2]/x - (x^2*Log[x])/9}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-5*y(x) = x^2*ln(x), y(x),'implicit')
Maple raw output
y(x) = x^5*_C2+1/x*_C1-1/9*x^2*ln(x)