72.15.15 problem 26

Internal problem ID [14896]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 07:18:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-\sqrt {2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+2*y(t)=0,y(0) = 3, D(y)(0) = -2^(1/2)],y(t), singsol=all)
 

\[ y = -\sin \left (\sqrt {2}\, t \right )+3 \cos \left (\sqrt {2}\, t \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+2*y[t]==0,{y[0]==3,Derivative[1][y][0] ==-Sqrt[2]}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 \cos \left (\sqrt {2} t\right )-\sin \left (\sqrt {2} t\right ) \]