35.6.9 problem 9

Internal problem ID [6159]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 9
Date solved : Monday, January 27, 2025 at 01:38:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 21

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

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