Internal problem ID [10962]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime }+16 y^{\prime }+17 y-17 t +1=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([4*diff(y(t),t$2)+16*diff(y(t),t)+17*y(t)=17*t-1,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = t +2 \,{\mathrm e}^{-2 t} \sin \left (\frac {t}{2}\right )-1 \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 21
DSolve[{4*y''[t]+16*y'[t]+17*y[t]==17*t-1,{y[0]==-1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t+2 e^{-2 t} \sin \left (\frac {t}{2}\right )-1 \\ \end{align*}