89.6.26 problem 26

Internal problem ID [24409]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 26
Date solved : Thursday, October 02, 2025 at 10:25:48 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -e^{\text {arctanh}(\cos (x))} \left (\arcsin (\cos (x))+\sqrt {\sin ^2(x)}-c_1\right ) \end{align*}

✗ Sympy

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

Timed Out