15.11.7 problem 7

Internal problem ID [3117]
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 : 7
Date solved : Monday, January 27, 2025 at 07:20:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 35

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

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