4.34.8 \(x^3 y''(x)=a+b x\)

ODE
\[ x^3 y''(x)=a+b x \] ODE Classification

[[_2nd_order, _quadrature]]

Book solution method
TO DO

Mathematica
cpu = 0.0115816 (sec), leaf count = 25

\[\left \{\left \{y(x)\to \frac {a}{2 x}-b \log (x)+c_2 x+c_1\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 20

\[ \left \{ y \left ( x \right ) =-b\ln \left ( x \right ) +{\frac {a}{2\,x}}+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input

DSolve[x^3*y''[x] == a + b*x,y[x],x]

Mathematica raw output

{{y[x] -> a/(2*x) + C[1] + x*C[2] - b*Log[x]}}

Maple raw input

dsolve(x^3*diff(diff(y(x),x),x) = b*x+a, y(x),'implicit')

Maple raw output

y(x) = -b*ln(x)+1/2/x*a+_C1*x+_C2