15.14.16 problem 16

Internal problem ID [3188]
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 : 16
Date solved : Monday, January 27, 2025 at 07:25:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

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

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_{1} +\frac {\left (5 x -2\right ) {\mathrm e}^{x}}{25} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{25} e^x (5 x-2)+c_1 \cos (2 x)+c_2 \sin (2 x) \]