Internal problem ID [5753]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section A,
Drill exercises. Page 309
Problem number: 3(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }-2 y+6 \,{\mathrm e}^{\pi -t}=0} \end {gather*} With initial conditions \begin {align*} [y \left (\pi \right ) = 1, y^{\prime }\left (\pi \right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 57
dsolve([diff(y(t),t$2)+3*diff(y(t),t)-2*y(t)=-6*exp(Pi-t),y(Pi) = 1, D(y)(Pi) = 4],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (19 \sqrt {17}-17\right ) {\mathrm e}^{\frac {\left (-3+\sqrt {17}\right ) \left (-\pi +t \right )}{2}}}{68}+\frac {\left (-19 \sqrt {17}-17\right ) {\mathrm e}^{\frac {\left (3+\sqrt {17}\right ) \left (\pi -t \right )}{2}}}{68}+\frac {3 \,{\mathrm e}^{\pi -t}}{2} \]
✓ Solution by Mathematica
Time used: 0.292 (sec). Leaf size: 103
DSolve[{y''[t]+3*y'[t]-2*y[t]==-6*Exp[Pi-t],{y[Pi]==1,y'[Pi]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{68} e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) t-\frac {1}{2} \left (\sqrt {17}-3\right ) \pi } \left (\left (19 \sqrt {17}-17\right ) e^{\sqrt {17} t}+102 e^{\frac {1}{2} \left (\left (1+\sqrt {17}\right ) t+\left (\sqrt {17}-1\right ) \pi \right )}-\left (\left (17+19 \sqrt {17}\right ) e^{\sqrt {17} \pi }\right )\right ) \\ \end{align*}