39.1.9 problem Problem 11.10

Internal problem ID [6514]
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
Date solved : Monday, January 27, 2025 at 02:11:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-5*y(x)=2*exp(5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\sqrt {5}\, x} c_2 +{\mathrm e}^{-\sqrt {5}\, x} c_1 +\frac {{\mathrm e}^{5 x}}{10} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]-5*y[x]==2*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{5 x}}{10}+c_1 e^{\sqrt {5} x}+c_2 e^{-\sqrt {5} x} \]