67.3.2 problem Problem 3

Internal problem ID [14020]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 3
Date solved : Tuesday, January 28, 2025 at 06:12:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.557 (sec). Leaf size: 15

dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+5*y(t)=0,y(0) = 2, D(y)(0) = 3],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 19

DSolve[{4*D[y[t],{t,2}]-4*D[y[t],t]+5*y[t]==0,{y[0]==2,Derivative[1][y][0] ==3}},y[t],t,IncludeSingularSolutions -> True]
 

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