67.4.6 problem Problem 2(f)

Internal problem ID [14050]
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(f)
Date solved : Tuesday, January 28, 2025 at 06:13:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 10.519 (sec). Leaf size: 36

dsolve([2*diff(y(t),t$2)-3*diff(y(t),t)+17*y(t)=17*t-1,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = \frac {125 \sqrt {127}\, \sin \left (\frac {\sqrt {127}\, t}{4}\right ) {\mathrm e}^{\frac {3 t}{4}}}{2159}-\frac {19 \,{\mathrm e}^{\frac {3 t}{4}} \cos \left (\frac {\sqrt {127}\, t}{4}\right )}{17}+t +\frac {2}{17} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 59

DSolve[{2*D[y[t],{t,2}]-3*D[y[t],t]+17*y[t]==17*t-1,{y[0]==-1,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t+\frac {125 e^{3 t/4} \sin \left (\frac {\sqrt {127} t}{4}\right )}{17 \sqrt {127}}-\frac {19}{17} e^{3 t/4} \cos \left (\frac {\sqrt {127} t}{4}\right )+\frac {2}{17} \]