52.6.5 problem 25

Internal problem ID [8340]
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 : 25
Date solved : Monday, January 27, 2025 at 03:49:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.556 (sec). Leaf size: 20

dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=t,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\left (30 t -2\right ) {\mathrm e}^{3 t}}{27}+\frac {t}{9}+\frac {2}{27} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==t,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{27} \left (3 t+e^{3 t} (30 t-2)+2\right ) \]