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 = 0.158443 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_2 x^5-\frac {1}{9} x^2 \log (x)+\frac {c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.103 (sec), leaf count = 22
\[\left [y \left (x \right ) = x^{5} \textit {\_C2} +\frac {\textit {\_C1}}{x}-\frac {x^{2} \ln \left (x \right )}{9}\right ]\] 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] -> C[1]/x + x^5*C[2] - (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))
Maple raw output
[y(x) = x^5*_C2+1/x*_C1-1/9*x^2*ln(x)]