35.8.13 problem 13

Internal problem ID [6220]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 13
Date solved : Monday, January 27, 2025 at 01:48:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=26 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=26*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==26*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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