56.1.4 problem 4

Internal problem ID [8716]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:24:34 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(y(x),x) = (5+sec(x)/x)*(sin(y(x))+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \int \frac {5 x +\sec \left (x \right )}{x}d x -\int _{}^{y}\frac {1}{\sin \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 21.094 (sec). Leaf size: 168

ode=D[y[x],x] == (5+Sec[x]/x)*(Sin[y[x]]+y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x\left (-\frac {2 \sec (K[1])}{K[1]}-\frac {5 (-\sec (K[1]) \sin (K[1]-y(x))+\sec (K[1]) \sin (K[1]+y(x))+2 y(x))}{\sin (y(x))+y(x)}\right )dK[1]+\int _1^{y(x)}\left (\frac {2}{K[2]+\sin (K[2])}-\int _1^x\left (\frac {5 (\cos (K[2])+1) (2 K[2]-\sec (K[1]) \sin (K[1]-K[2])+\sec (K[1]) \sin (K[1]+K[2]))}{(K[2]+\sin (K[2]))^2}-\frac {5 (\cos (K[1]-K[2]) \sec (K[1])+\cos (K[1]+K[2]) \sec (K[1])+2)}{K[2]+\sin (K[2])}\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.570 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-5 - 1/(x*cos(x)))*(y(x) + sin(y(x))) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{y + \sin {\left (y \right )}}\, dy = C_{1} + \int \frac {5 x \cos {\left (x \right )} + 1}{x \cos {\left (x \right )}}\, dx \]