32.8.17 problem Exercise 21.21, page 231

Internal problem ID [5966]
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 21.21, page 231
Date solved : Monday, January 27, 2025 at 01:29:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=x +{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=x+exp(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} \left (\left (-\frac {6 x}{5}-6 c_{1} +\frac {6}{25}\right ) {\mathrm e}^{5 x}+\left (x +\frac {1}{6}\right ) {\mathrm e}^{3 x}-6 c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]+D[y[x],x]-6*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{36} (-6 x-1)+c_1 e^{-3 x}+e^{2 x} \left (\frac {x}{5}-\frac {1}{25}+c_2\right ) \]