52.6.10 problem 30

Internal problem ID [8345]
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 : 30
Date solved : Monday, January 27, 2025 at 03:49:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=1+t \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.650 (sec). Leaf size: 25

dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=1+t,y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
 

\[ y = \frac {51 \,{\mathrm e}^{t} \sin \left (2 t \right )}{25}-\frac {7 \,{\mathrm e}^{t} \cos \left (2 t \right )}{25}+\frac {t}{5}+\frac {7}{25} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 32

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]+5*y[t]==1+t,{y[0]==0,Derivative[1][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{25} \left (5 t+51 e^t \sin (2 t)-7 e^t \cos (2 t)+7\right ) \]