60.1.526 problem 539

Internal problem ID [10540]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 539
Date solved : Sunday, March 30, 2025 at 05:49:08 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 32

ode:=diff(y(x),x)^3*sin(x)-(sin(x)*y(x)-cos(x)^2)*diff(y(x),x)^2-(y(x)*cos(x)^2+sin(x))*diff(y(x),x)+sin(x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,{\mathrm e}^{x} \\ y &= -\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+c_1 \\ y &= -\cos \left (x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 38

ode=Sin[x]*y[x] - (Sin[x] + Cos[x]^2*y[x])*D[y[x],x] - (-Cos[x]^2 + Sin[x]*y[x])*D[y[x],x]^2 + Sin[x]*D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 e^x \\ y(x)\to \text {arctanh}(\cos (x))+c_1 \\ y(x)\to \int _1^x\sin (K[1])dK[1]+c_1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-y(x)*sin(x) + cos(x)**2)*Derivative(y(x), x)**2 - (y(x)*cos(x)**2 + sin(x))*Derivative(y(x), x) + y(x)*sin(x) + sin(x)*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out