Internal problem ID [10999]
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(c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y-8 \,{\mathrm e}^{2 t}+5 \,{\mathrm e}^{t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(t),t$3)-diff(y(t),t$2)+4*diff(y(t),t)-4*y(t)=8*exp(2*t)-5*exp(t),y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t}-{\mathrm e}^{t} t +{\mathrm e}^{t}-\sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.353 (sec). Leaf size: 24
DSolve[{y'''[t]-y''[t]+4*y'[t]-4*y[t]==8*Exp[2*t]-5*Exp[t],{y[0]==2,y'[0]==0,y''[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (-t+e^t+1\right )-\sin (2 t) \\ \end{align*}