32.8.21 problem Exercise 21.28, page 231

Internal problem ID [5970]
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 21.28, page 231
Date solved : Monday, January 27, 2025 at 01:29:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)-5*diff(y(x),x)-6*y(x)=exp(3*x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {10 \,{\mathrm e}^{6 x}}{21}+\frac {45 \,{\mathrm e}^{-x}}{28}-\frac {{\mathrm e}^{3 x}}{12} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 30

DSolve[{D[y[x],{x,2}]-5*D[y[x],x]-6*y[x]==Exp[3*x],{y[0]==2,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{84} e^{-x} \left (-7 e^{4 x}+40 e^{7 x}+135\right ) \]