60.1.197 problem 200

Internal problem ID [10211]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 200
Date solved : Wednesday, March 05, 2025 at 08:43:19 AM
CAS classification : [_linear]

\begin{align*} \left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 53

ode:=(a*sin(x)^2+b)*diff(y(x),x)+a*y(x)*sin(2*x)+A*x*(a*sin(x)^2+c) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-A a \cos \left (2 x \right )-2 A x a \sin \left (2 x \right )+2 x^{2} \left (a +2 c \right ) A -8 c_{1}}{4 a \cos \left (2 x \right )-4 a -8 b} \]

✓ Mathematica. Time used: 0.569 (sec). Leaf size: 48

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

\[ y(x)\to \frac {\int _1^xA (-\cos (2 K[1]) a+a+2 c) K[1]dK[1]+c_1}{a \cos (2 x)-a-2 b} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(A*x*(a*sin(x)**2 + c) + a*y(x)*sin(2*x) + (a*sin(x)**2 + b)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out