72.19.1 problem 27

Internal problem ID [14959]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 6. Laplace transform. Section 6.3 page 600
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 07:25:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=8 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=11\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 8.779 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+4*y(t)=8,y(0) = 11, D(y)(0) = 5],y(t), singsol=all)
 

\[ y = 9 \cos \left (2 t \right )+\frac {5 \sin \left (2 t \right )}{2}+2 \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]+4*y[t]==8,{y[0]==11,Derivative[1][y][0] ==5}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 9 \cos (2 t)+5 \sin (t) \cos (t)+2 \]