4.29.20 \(x^2 y''(x)=a+b x\)

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]