ODE
\[ x^2 y''(x)-3 x y'(x)+4 y(x)=5 x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163757 (sec), leaf count = 20
\[\{\{y(x)\to x (c_1 x+2 c_2 x \log (x)+5)\}\}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 20
\[[y \left (x \right ) = x^{2} \textit {\_C2} +x^{2} \ln \left (x \right ) \textit {\_C1} +5 x]\] Mathematica raw input
DSolve[4*y[x] - 3*x*y'[x] + x^2*y''[x] == 5*x,y[x],x]
Mathematica raw output
{{y[x] -> x*(5 + x*C[1] + 2*x*C[2]*Log[x])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 5*x, y(x))
Maple raw output
[y(x) = x^2*_C2+x^2*ln(x)*_C1+5*x]