15.1.12 problem 12

Internal problem ID [2852]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 02:51:16 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=1-\sin \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(x(t),t) = 1-sin(2*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = \frac {\cos \left (2 t \right )}{2}+t +c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 17

ode=D[x[t],t]==1-Sin[2*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to t+\frac {1}{2} \cos (2 t)+c_1 \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 12

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

\[ x{\left (t \right )} = C_{1} + t + \frac {\cos {\left (2 t \right )}}{2} \]