84.8.6 problem 4.15

Internal problem ID [22118]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.15
Date solved : Thursday, October 02, 2025 at 08:25:26 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.188 (sec). Leaf size: 14

ode:=sin(x)+y(x)*diff(y(x),x) = 0; 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\sqrt {2 \cos \left (x \right )+2} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to -\sqrt {2} \sqrt {\cos (x)+1} \end{align*}

✓ Sympy. Time used: 0.333 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \sqrt {2 \cos {\left (x \right )} + 2} \]