29.5.9 problem 125

Internal problem ID [4726]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 125
Date solved : Sunday, March 30, 2025 at 03:50:16 AM
CAS classification : unknown

\begin{align*} y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \end{align*}

✗ Maple

ode:=diff(y(x),x) = (1+cos(x)*sin(y(x)))*tan(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 1.857 (sec). Leaf size: 58

ode=D[y[x],x]==(1+Cos[x] Sin[y[x]])Tan[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \csc ^{-1}\left (\frac {1}{2} \left (-\sin (x)-\cos (x)-2 c_1 e^{-x}\right )\right ) \\ y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 5.713 (sec). Leaf size: 53

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

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\frac {2 e^{x}}{C_{1} + \sqrt {2} e^{x} \sin {\left (x + \frac {\pi }{4} \right )}} \right )} + \pi , \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {2 e^{x}}{C_{1} - \sqrt {2} e^{x} \sin {\left (x + \frac {\pi }{4} \right )}} \right )}\right ] \]