67.4.6 problem Problem 2(f)

Internal problem ID [13979]
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 : Monday, March 31, 2025 at 08:20:44 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*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 36

ode:=2*diff(diff(y(t),t),t)-3*diff(y(t),t)+17*y(t) = 17*t-1; 
ic:=y(0) = -1, D(y)(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 46

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-17*t + 17*y(t) - 3*Derivative(y(t), t) + 2*Derivative(y(t), (t, 2)) + 1,0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

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