Internal problem ID [12306]
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 25.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 4, y^{\prime \prime }\left (0\right ) = -24] \end {align*}
✓ Solution by Maple
Time used: 4.656 (sec). Leaf size: 15
dsolve([diff(y(t),t$3)+6*diff(y(t),t$2)+25*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 4, (D@@2)(y)(0) = -24],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-3 t} \sin \left (4 t \right )+1 \]
✓ Solution by Mathematica
Time used: 0.467 (sec). Leaf size: 17
DSolve[{y'''[t]+6*y''[t]+25*y'[t]==0,{y[0]==1,y'[0]==4,y''[0]==-24}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \sin (4 t)+1 \]