52.5.6 problem 36

Internal problem ID [8329]
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
Date solved : Monday, January 27, 2025 at 03:49:06 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.686 (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)
 

\[ y = \frac {11 \,{\mathrm e}^{4 t}}{10}-2 \,{\mathrm e}^{3 t}-\frac {3 \,{\mathrm e}^{-t}}{5}+\frac {5}{2} \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 34

DSolve[{D[y[t],{t,2}]-4*D[y[t],t]==6*Exp[3*t]-3*Exp[-t],{y[0]==1,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {3 e^{-t}}{5}-2 e^{3 t}+\frac {11 e^{4 t}}{10}+\frac {5}{2} \]