Internal problem ID [2509]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-3 y-{\mathrm e}^{3 x}-{\mathrm e}^{-3 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (5) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 31
dsolve([diff(y(x),x)-3*y(x)=exp(3*x)+exp(-3*x),y(5) = 5],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (6 x \,{\mathrm e}^{6 x +30}-30 \,{\mathrm e}^{6 x +30}+30 \,{\mathrm e}^{15+6 x}-{\mathrm e}^{30}+{\mathrm e}^{6 x}\right ) {\mathrm e}^{-3 x -30}}{6} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 39
DSolve[{y'[x]-3*y[x]==Exp[3*x]+Exp[-3*x],y[5]==5},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-3 x} \left (e^{6 (x-5)} \left (6 e^{30} (x-5)+30 e^{15}+1\right )-1\right ) \\ \end{align*}