Internal problem ID [4663]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y-2 \,{\mathrm e}^{5 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-5*y(x)=2*exp(5*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\sqrt {5}\, x} c_{2}+{\mathrm e}^{-\sqrt {5}\, x} c_{1}+\frac {{\mathrm e}^{5 x}}{10} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 40
DSolve[y''[x]-5*y[x]==2*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{5 x}}{10}+c_1 e^{\sqrt {5} x}+c_2 e^{-\sqrt {5} x} \\ \end{align*}