23.1.17 problem 2(g)

Internal problem ID [4107]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(g)
Date solved : Monday, January 27, 2025 at 08:09:01 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (5\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.094 (sec). Leaf size: 35

dsolve([diff(y(x),x)-3*y(x)=exp(3*x)+exp(-3*x),y(5) = 5],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x -30}}{6}+5 \,{\mathrm e}^{3 x -15}+\left (x -5\right ) {\mathrm e}^{3 x}-\frac {{\mathrm e}^{-3 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 48

DSolve[{D[y[x],x]-3*y[x]==Exp[3*x]+Exp[-3*x],y[5]==5},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-3 (x+10)} \left (6 e^{6 (x+5)} (x-5)+e^{6 x}+30 e^{6 x+15}-e^{30}\right ) \]