64.20.10 problem 10

Internal problem ID [13653]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:54:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 t \,{\mathrm e}^{2 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 8.331 (sec). Leaf size: 27

dsolve([diff(y(t),t$2)-8*diff(y(t),t)+15*y(t)=9*t*exp(2*t),y(0) = 5, D(y)(0) = 10],y(t), singsol=all)
 

\[ y = \left (3 t +4\right ) {\mathrm e}^{2 t}+3 \,{\mathrm e}^{3 t}-2 \,{\mathrm e}^{5 t} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]-8*D[y[t],t]+15*y[t]==9*t*Exp[2*t],{y[0]==5,Derivative[1][y][0]==10}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t} \left (3 t+3 e^t-2 e^{3 t}+4\right ) \]