15.11.4 problem 4

Internal problem ID [3114]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:19:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y = -\left ({\mathrm e}^{-x} \left (x +c_{1} +1\right )-c_2 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

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

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