68.4.14 problem 14

Internal problem ID [17194]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 14
Date solved : Thursday, October 02, 2025 at 01:50:06 PM
CAS classification : [_separable]

\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 28

ode:=(5*x(t)^5-4*cos(x(t)))*diff(x(t),t)+2*cos(9*t)+2*sin(7*t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \frac {\sin \left (9 t \right )}{9}-\frac {\cos \left (7 t \right )}{7}+\frac {5 x^{6}}{12}-2 \sin \left (x\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.385 (sec). Leaf size: 50

ode=(5*x[t]^5-4*Cos[x[t]])*D[x[t],t]+(2*Cos[9*t]+2*Sin[7*t])==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\left (5 K[1]^5-4 \cos (K[1])\right )dK[1]\&\right ]\left [\int _1^t-2 (\cos (9 K[2])+\sin (7 K[2]))dK[2]+c_1\right ] \end{align*}

✓ Sympy. Time used: 10.206 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((5*x(t)**5 - 4*cos(x(t)))*Derivative(x(t), t) + 2*sin(7*t) + 2*cos(9*t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ \frac {5 x^{6}{\left (t \right )}}{6} + \frac {2 \sin {\left (9 t \right )}}{9} - 4 \sin {\left (x{\left (t \right )} \right )} - \frac {2 \cos {\left (7 t \right )}}{7} = C_{1} \]