67.3.29 problem 4.7 (c)

Internal problem ID [16350]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (c)
Date solved : Thursday, October 02, 2025 at 01:22:04 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = -\frac {1}{\cos \left (x \right )-c_1 +3 x} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to -\frac {1}{\int _1^x(3-\sin (K[1]))dK[1]+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \frac {1}{C_{1} + 3 x + \cos {\left (x \right )}} \]