Internal problem ID [3018]
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`]]
\[ \boxed {y^{\prime }-3 y={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}} \] With initial conditions \begin {align*} [y \left (5\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.109 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x -30}}{6}+5 \,{\mathrm e}^{3 x -15}+\left (x -5\right ) {\mathrm e}^{3 x}-\frac {{\mathrm e}^{-3 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 48
DSolve[{y'[x]-3*y[x]==Exp[3*x]+Exp[-3*x],y[5]==5},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-3 (x+10)} \left (6 e^{6 (x+5)} (x-5)+e^{6 x}+30 e^{6 x+15}-e^{30}\right ) \]