Internal problem ID [6661]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 1.812 (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)
\[ y \left (t \right ) = \frac {5}{2}+\frac {11 \,{\mathrm e}^{4 t}}{10}-2 \,{\mathrm e}^{3 t}-\frac {3 \,{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.139 (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]
\[ y(t)\to -\frac {3 e^{-t}}{5}-2 e^{3 t}+\frac {11 e^{4 t}}{10}+\frac {5}{2} \]