90.1.27 problem 38

Internal problem ID [25051]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 38
Date solved : Thursday, October 02, 2025 at 11:47:53 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=6 \sin \left (3 t \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t) = 6*sin(3*t); 
ic:=[y(0) = 1, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {2 \sin \left (3 t \right )}{3}+4 t +1 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=D[y[t],{t,2}]== 6*Sin[3*t]; 
ic={y[0]==1,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 4 t-\frac {2}{3} \sin (3 t)+1 \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*sin(3*t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 4 t - \frac {2 \sin {\left (3 t \right )}}{3} + 1 \]