32.8.25 problem Exercise 21.33, page 231

Internal problem ID [5974]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.33, page 231
Date solved : Monday, January 27, 2025 at 01:29:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(-x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {5 \,{\mathrm e}^{2 x}}{3}+\frac {5 \,{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{6} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 31

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Exp[-x],{y[0]==1,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x}}{6}+\frac {5 e^x}{2}-\frac {5 e^{2 x}}{3} \]