38.3.3 problem 3

Internal problem ID [6481]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:07:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{-x}+{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 24

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

\[ y(x)\to e^{-2 x} \left (1+e^x (c_2 x+c_1)\right ) \]