Internal problem ID [10998]
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 13(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y-4 t=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -2, y^{\prime \prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve([diff(y(t),t$3)-2*diff(y(t),t$2)-diff(y(t),t)+2*y(t)=4*t,y(0) = 2, D(y)(0) = -2, (D@@2)(y)(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = 2 t +1-3 \,{\mathrm e}^{t}+3 \,{\mathrm e}^{-t}+{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[{y'''[t]-2*y''[t]-y'[t]+2*y[t]==4*t,{y[0]==2,y'[0]==-2,y''[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 t-6 \sinh (t)+\sinh (2 t)+\cosh (2 t)+1 \\ \end{align*}