Internal problem ID [6508]
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]]
\[ \boxed {y^{\prime \prime }-y^{\prime }+y=3 \,{\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (t \right ) = \frac {\left (4 \,{\mathrm e}^{\frac {3 t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) \sqrt {3}+6 \,{\mathrm e}^{\frac {3 t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right )+3\right ) {\mathrm e}^{-t}}{3} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 56
DSolve[{y''[t]-y'[t]+y[t]==3*Exp[-t],{y[0]==3,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t}+\frac {4 e^{t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )}{\sqrt {3}}+2 e^{t/2} \cos \left (\frac {\sqrt {3} t}{2}\right ) \]