60.1.352 problem 359

Internal problem ID [10366]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 359
Date solved : Wednesday, March 05, 2025 at 10:37:42 AM
CAS classification : [_separable]

\begin{align*} 3 y^{\prime } \sin \left (x \right ) \sin \left (y\right )+5 \cos \left (x \right )^{4} y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 26

ode:=3*diff(y(x),x)*sin(x)*sin(y(x))+5*cos(x)^4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {3 \,\operatorname {Si}\left (y\right )}{5}+c_{1} +\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+\frac {\cos \left (x \right )^{3}}{3}+\cos \left (x \right ) = 0 \]

✓ Mathematica. Time used: 0.608 (sec). Leaf size: 50

ode=5*Cos[x]^4*y[x] + 3*Sin[x]*Sin[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sin (K[1])}{K[1]}dK[1]\&\right ]\left [\int _1^x-\frac {5}{3} \cos ^3(K[2]) \cot (K[2])dK[2]+c_1\right ] \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.651 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x)*cos(x)**4 + 3*sin(x)*sin(y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \operatorname {Si}{\left (y{\left (x \right )} \right )} = C_{1} - \frac {5 \log {\left (\cos {\left (x \right )} - 1 \right )}}{6} + \frac {5 \log {\left (\cos {\left (x \right )} + 1 \right )}}{6} - \frac {5 \cos ^{3}{\left (x \right )}}{9} - \frac {5 \cos {\left (x \right )}}{3} \]