Internal problem ID [2239]
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 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 28.
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-5 \,{\mathrm e}^{2 x}=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)=5*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+c_{1} {\mathrm e}^{2 x}+\frac {5 \,{\mathrm e}^{2 x} x}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y''[x]-y'[x]-2*y[x]==5*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+e^{2 x} \left (\frac {5 x}{3}-\frac {5}{9}+c_2\right ) \\ \end{align*}