3.2 problem Problem 3

Internal problem ID [10936]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}

Solution by Maple

Time used: 0.0 (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)
 

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

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 19

DSolve[{4*y''[t]-4*y'[t]+5*y[t]==0,{y[0]==2,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to 2 e^{t/2} (\sin (t)+\cos (t)) \\ \end{align*}