Internal problem ID [2236]
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 25.
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-6 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+y(x)=6*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+c_{1} \cos \relax (x )+3 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 21
DSolve[y''[x]+y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 e^x+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}