52.5.12 problem 42

Internal problem ID [8335]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 42
Date solved : Monday, January 27, 2025 at 03:49:10 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.623 (sec). Leaf size: 16

dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=0,y(0) = 1, D(y)(0) = 3],y(t), singsol=all)
 

\[ y = {\mathrm e}^{t} \left (\sin \left (2 t \right )+\cos \left (2 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]+5*y[t]==0,{y[0]==1,Derivative[1][y][0] ==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t (\sin (2 t)+\cos (2 t)) \]