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`]]
\[ \boxed {y^{\prime }-3 y-{\mathrm e}^{3 x}-{\mathrm e}^{-3 x}=0} \] With initial conditions \begin {align*} [y \left (5\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x -30}}{6}+5 \,{\mathrm e}^{3 x -15}+\left (-5+x \right ) {\mathrm e}^{3 x}-\frac {{\mathrm e}^{-3 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.071 (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*}