Internal problem ID [5911]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES
Page 289
Problem number: 39.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y-{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 28
dsolve([2*diff(y(t),t$3)+3*diff(y(t),t$2)-3*diff(y(t),t)-2*y(t)=exp(-t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (5 \,{\mathrm e}^{3 t}-16 \,{\mathrm e}^{\frac {3 t}{2}}+9 \,{\mathrm e}^{t}+2\right ) {\mathrm e}^{-2 t}}{18} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 37
DSolve[{2*y'''[t]+3*y''[t]-3*y'[t]-2*y[t]==Exp[-t],{y[0]==0,y'[0]==0,y''[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{18} e^{-2 t} \left (9 e^t-16 e^{3 t/2}+5 e^{3 t}+2\right ) \\ \end{align*}