82.27.3 problem Ex. 3

Internal problem ID [18878]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 73
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:33:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}+\frac {2 \,{\mathrm e}^{2 x}}{9} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 28

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

\[ y(x)\to \frac {2 e^{2 x}}{9}+e^{-x} (c_2 x+c_1) \]