56.1.3 problem 3

Internal problem ID [8715]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 3
Date solved : Wednesday, March 05, 2025 at 06:13:22 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(y(x),x) = sec(x)*(sin(y(x))+y(x))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ \int \frac {\sec \left (x \right )}{x}d x -\int _{}^{y}\frac {1}{\sin \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +c_{1} = 0 \]

✓ Mathematica. Time used: 0.977 (sec). Leaf size: 41

ode=D[y[x],x]== Sec[x]*(Sin[y[x]]+y[x])/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]+\sin (K[1])}dK[1]\&\right ]\left [\int _1^x\frac {\sec (K[2])}{K[2]}dK[2]+c_1\right ] \]

✓ Sympy. Time used: 0.545 (sec). Leaf size: 19

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

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{y + \sin {\left (y \right )}}\, dy = C_{1} + \int \frac {1}{x \cos {\left (x \right )}}\, dx \]