15.14.1 problem 1

Internal problem ID [3173]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:24:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_{1} +\frac {2 \,{\mathrm e}^{x}}{5} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

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

\[ y(x)\to \frac {2 e^x}{5}+c_1 \cos (2 x)+c_2 \sin (2 x) \]