60.1.32 problem 32

Internal problem ID [10046]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 32
Date solved : Sunday, March 30, 2025 at 02:55:24 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.290 (sec). Leaf size: 27

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

\[ y = \frac {-2 \cos \left (x \right )^{2} c_1 -2 \sec \left (x \right )}{\cos \left (x \right )^{3} c_1 -2} \]

✓ Mathematica. Time used: 0.79 (sec). Leaf size: 32

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

\begin{align*} y(x)\to \frac {\sec (x) \left (-2 \cos ^3(x)+c_1\right )}{\cos ^3(x)+c_1} \\ y(x)\to \sec (x) \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -(-y(x)**2 + 2/cos(x)**2)*sin(x) + Derivative(y(x), x) cannot be solved by the factorable group method