50.25.6 problem 4(b)

Internal problem ID [8178]
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)
Date solved : Monday, January 27, 2025 at 03:45:17 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=2 \end{align*}

Using Laplace method

✓ Solution by Maple

Time used: 0.670 (sec). Leaf size: 48

dsolve(diff(y(t),t$2)+3*diff(y(t),t)+3*y(t)=2,y(t), singsol=all)
 

\[ y = \frac {2}{3}+\frac {\left (\cos \left (\frac {\sqrt {3}\, t}{2}\right ) \left (-2+3 y \left (0\right )\right )+\sin \left (\frac {\sqrt {3}\, t}{2}\right ) \sqrt {3}\, \left (2 y^{\prime }\left (0\right )+3 y \left (0\right )-2\right )\right ) {\mathrm e}^{-\frac {3 t}{2}}}{3} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 51

DSolve[D[y[t],{t,2}]+3*D[y[t],t]+3*y[t]==2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_2 e^{-3 t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 e^{-3 t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )+\frac {2}{3} \]