Internal problem ID [2232]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y-4 x^{2}-5=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=4*x^2+5,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{-2 x} c_{1}-2 x^{2}-2 x -\frac {11}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 29
DSolve[y''[x]+y'[x]-2*y[x]==4*x^2+5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x (x+1)+c_1 e^{-2 x}+c_2 e^x-\frac {11}{2} \\ \end{align*}