Internal problem ID [5912]
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: 40.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y-\sin \left (3 t \right )=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: 0.018 (sec). Leaf size: 33
dsolve([diff(y(t),t$3)+2*diff(y(t),t$2)-diff(y(t),t)-2*y(t)=sin(3*t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (169 \,{\mathrm e}^{3 t}-12 \sin \left (3 t \right ) {\mathrm e}^{2 t}+18 \cos \left (3 t \right ) {\mathrm e}^{2 t}-507 \,{\mathrm e}^{t}+320\right ) {\mathrm e}^{-2 t}}{780} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 42
DSolve[{y'''[t]+2*y''[t]-y'[t]-2*y[t]==Sin[3*t],{y[0]==0,y'[0]==0,y''[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{780} \left (e^{-2 t} \left (169 e^t \left (e^{2 t}-3\right )+320\right )-12 \sin (3 t)+18 \cos (3 t)\right ) \\ \end{align*}