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 = 0.0106962 (sec), leaf count = 20
\[\left \{\left \{y(x)\to x \left (c_1 x+2 c_2 x \log (x)+5\right )\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={x}^{2}{\it \_C2}+{x}^{2}\ln \left ( x \right ) {\it \_C1}+5\,x \right \} \] 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),'implicit')
Maple raw output
y(x) = x^2*_C2+x^2*ln(x)*_C1+5*x