81.1.12 problem 11

Internal problem ID [18607]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 12:03:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=2 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

\[ y \left (x \right ) = \frac {\left (2 \,{\mathrm e}^{5 x}+15 c_{1} {\mathrm e}^{2 x}+15 c_{2} \right ) {\mathrm e}^{-3 x}}{15} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 31

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

\[ y(x)\to \frac {2 e^{2 x}}{15}+c_1 e^{-3 x}+c_2 e^{-x} \]