54.1.195 problem 198

Internal problem ID [11509]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 198
Date solved : Tuesday, September 30, 2025 at 08:53:42 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = -\sin \left (x \right )+\tan \left (x \right ) c_1 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \tan (x) \left (\int _1^x\sin (K[1])dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

Timed Out