15.14.4 problem 4

Internal problem ID [3176]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:25:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

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

\[ y = -\frac {\left (-3 c_2 \,{\mathrm e}^{3 x}-3 c_{1} +x \right ) {\mathrm e}^{-2 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{9} e^{-2 x} \left (-3 x+9 c_2 e^{3 x}-1+9 c_1\right ) \]