Internal problem ID [5908]
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: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }-6 \,{\mathrm e}^{3 t}+3 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)-4*diff(y(t),t)=6*exp(3*t)-3*exp(-t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = \frac {11 \,{\mathrm e}^{4 t}}{10}-\frac {3 \,{\mathrm e}^{-t}}{5}-2 \,{\mathrm e}^{3 t}+\frac {5}{2} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 34
DSolve[{y''[t]-4*y'[t]==6*Exp[3*t]-3*Exp[-t],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {3 e^{-t}}{5}-2 e^{3 t}+\frac {11 e^{4 t}}{10}+\frac {5}{2} \\ \end{align*}