15.14.15 problem 15

Internal problem ID [3187]
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 : 15
Date solved : Monday, January 27, 2025 at 07:25:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

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

\[ y = \frac {\left (4 c_2 \,{\mathrm e}^{3 x}+\left (-2 x +1\right ) {\mathrm e}^{x}+4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{4} e^{-x} (1-2 x)+c_1 e^{-2 x}+c_2 e^x \]