Internal problem ID [5755]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }+y-3 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 38
dsolve([diff(y(t),t$2)-diff(y(t),t)+y(t)=3*exp(-t),y(0) = 3, D(y)(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {4 \sqrt {3}\, {\mathrm e}^{\frac {3 t}{2}} {\mathrm e}^{-t} \sin \left (\frac {\sqrt {3}\, t}{2}\right )}{3}+2 \,{\mathrm e}^{\frac {3 t}{2}} {\mathrm e}^{-t} \cos \left (\frac {\sqrt {3}\, t}{2}\right )+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 54
DSolve[{y''[t]-y'[t]+y[t]==3*Exp[-t],{y[0]==3,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t}+\frac {2}{3} e^{t/2} \left (2 \sqrt {3} \sin \left (\frac {\sqrt {3} t}{2}\right )+3 \cos \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}