52.6.4 problem 24

Internal problem ID [8339]
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. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 24
Date solved : Monday, January 27, 2025 at 03:49:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.611 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=t^3*exp(2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {t^{5} {\mathrm e}^{2 t}}{20} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 17

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

\[ y(t)\to \frac {1}{20} e^{2 t} t^5 \]