4.25.2 \(y''(x)=a x+b y(x)\)

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.155965 (sec), leaf count = 38

\[\left \{\left \{y(x)\to -\frac {a x}{b}+c_1 e^{\sqrt {b} x}+c_2 e^{-\sqrt {b} x}\right \}\right \}\]

Maple
cpu = 0.023 (sec), leaf count = 29

\[\left [y \left (x \right ) = {\mathrm e}^{x \sqrt {b}} \textit {\_C2} +{\mathrm e}^{-x \sqrt {b}} \textit {\_C1} -\frac {a x}{b}\right ]\] Mathematica raw input

DSolve[y''[x] == a*x + b*y[x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(y(x),x),x) = a*x+b*y(x), y(x))

Maple raw output

[y(x) = exp(x*b^(1/2))*_C2+exp(-x*b^(1/2))*_C1-a/b*x]