90.9.3 problem 35

Internal problem ID [25191]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 2. The Laplace Transform. Exercises at page 139
Problem number : 35
Date solved : Thursday, October 02, 2025 at 11:57:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)-5*y(t) = 150*t; 
ic:=[y(0) = -1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -30 t +24-26 \,{\mathrm e}^{-t}+{\mathrm e}^{5 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=D[y[t],{t,2}]-4*D[y[t],{t,1}]-5*y[t]==150*t; 
ic={y[0]==-1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -30 t-26 e^{-t}+e^{5 t}+24 \end{align*}

✓ Sympy. Time used: 0.051 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-150*t - 5*y(t) - 3*Derivative(y(t), (t, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 30 t + \frac {31 \sqrt {15} \sin {\left (\frac {\sqrt {15} t}{3} \right )}}{5} - \cos {\left (\frac {\sqrt {15} t}{3} \right )} \]