Internal problem ID [6664]
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]]
\[ \boxed {2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y={\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.859 (sec). Leaf size: 25
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)
\[ y \left (t \right ) = \frac {7 \cosh \left (t \right )}{9}-\frac {2 \sinh \left (t \right )}{9}+\frac {{\mathrm e}^{-2 t}}{9}-\frac {8 \,{\mathrm e}^{-\frac {t}{2}}}{9} \]
✓ Solution by Mathematica
Time used: 0.008 (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]
\[ y(t)\to \frac {1}{18} e^{-2 t} \left (9 e^t-16 e^{3 t/2}+5 e^{3 t}+2\right ) \]