67.4.8 problem Problem 2(h)

Internal problem ID [14052]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 2(h)
Date solved : Tuesday, January 28, 2025 at 06:13:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 9.107 (sec). Leaf size: 25

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

\[ y = -\frac {34 \sin \left (2 t \right ) {\mathrm e}^{t}}{25}+\frac {88 \cos \left (2 t \right ) {\mathrm e}^{t}}{25}+\frac {t}{5}+\frac {12}{25} \]

✓ 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]==2+t,{y[0]==4,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{25} \left (5 t-34 e^t \sin (2 t)+88 e^t \cos (2 t)+12\right ) \]