84.5.9 problem 3.3 (a)

Internal problem ID [22096]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.3 (a)
Date solved : Thursday, October 02, 2025 at 08:24:43 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 54

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

\begin{align*} y &= \left (3 \cos \left (x \right )+c_1 \right )^{{1}/{3}} \\ y &= -\frac {\left (3 \cos \left (x \right )+c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left (3 \cos \left (x \right )+c_1 \right )^{{1}/{3}} \left (-1+i \sqrt {3}\right )}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 64

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

\begin{align*} y(x)&\to -\sqrt [3]{-3} \sqrt [3]{\cos (x)+c_1}\\ y(x)&\to \sqrt [3]{3} \sqrt [3]{\cos (x)+c_1}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{3} \sqrt [3]{\cos (x)+c_1} \end{align*}

✓ Sympy. Time used: 1.110 (sec). Leaf size: 61

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

\[ \left [ y{\left (x \right )} = \sqrt [3]{C_{1} + 3 \cos {\left (x \right )}}, \ y{\left (x \right )} = \frac {\left (- \sqrt [3]{3} - 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + \cos {\left (x \right )}}}{2}, \ y{\left (x \right )} = \frac {\left (- \sqrt [3]{3} + 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + \cos {\left (x \right )}}}{2}\right ] \]