ODE
\[ x^2 y''(x)=a+b x \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162288 (sec), leaf count = 26
\[\{\{y(x)\to \log (x) (b x-a)-b x+c_2 x+c_1\}\}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 23
\[[y \left (x \right ) = b \ln \left (x \right ) x -b x -a \ln \left (x \right )+\textit {\_C1} x +\textit {\_C2}]\] Mathematica raw input
DSolve[x^2*y''[x] == a + b*x,y[x],x]
Mathematica raw output
{{y[x] -> -(b*x) + C[1] + x*C[2] + (-a + b*x)*Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = b*x+a, y(x))
Maple raw output
[y(x) = b*ln(x)*x-b*x-a*ln(x)+_C1*x+_C2]