78.16.1 problem 1

Internal problem ID [18380]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:48:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-4*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (x +4 c_{2} \right ) {\mathrm e}^{2 x}}{4}+{\mathrm e}^{-2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-4*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\frac {x}{4}-\frac {1}{16}+c_1\right )+c_2 e^{-2 x} \]