Internal problem ID [5757]
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: 4(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+3 y-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 32
dsolve(diff(y(t),t$2)+3*diff(y(t),t)+3*y(t)=2,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_{2}+{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_{1}+\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 46
DSolve[y''[t]+3*y'[t]+3*y[t]==2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2}{3}+e^{-3 t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}