44.25.1 problem 3(a)

Internal problem ID [9459]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section A, Drill exercises. Page 309
Problem number : 3(a)
Date solved : Tuesday, September 30, 2025 at 06:19:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-5 y&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.142 (sec). Leaf size: 35

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-5*y(t) = 1; 
ic:=[y(0) = 0, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {13 \sinh \left (\frac {t \sqrt {29}}{2}\right ) {\mathrm e}^{-\frac {3 t}{2}} \sqrt {29}}{145}+\frac {\cosh \left (\frac {t \sqrt {29}}{2}\right ) {\mathrm e}^{-\frac {3 t}{2}}}{5}-\frac {1}{5} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 67

ode=D[y[t],{t,2}]+3*D[y[t],t]-5*y[t]==1; 
ic={y[0]==0,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{290} e^{-\frac {1}{2} \left (3+\sqrt {29}\right ) t} \left (\left (29+13 \sqrt {29}\right ) e^{\sqrt {29} t}-58 e^{\frac {1}{2} \left (3+\sqrt {29}\right ) t}+29-13 \sqrt {29}\right ) \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 53

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-5*y(t) + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 1,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {1}{10} + \frac {13 \sqrt {29}}{290}\right ) e^{\frac {t \left (-3 + \sqrt {29}\right )}{2}} - \frac {1}{5} + \left (\frac {1}{10} - \frac {13 \sqrt {29}}{290}\right ) e^{- \frac {t \left (3 + \sqrt {29}\right )}{2}} \]