67.3.43 problem 4.8 (b)

Internal problem ID [16364]
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 : 4.8 (b)
Date solved : Thursday, October 02, 2025 at 01:22:37 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.227 (sec). Leaf size: 14

ode:=y(x)*diff(y(x),x) = sin(x); 
ic:=[y(0) = -4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\sqrt {18-2 \cos \left (x \right )} \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 28

ode=y[x]*D[y[x],x]==Sin[x]; 
ic={y[0]==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {2} \sqrt {\int _0^x\sin (K[1])dK[1]+8} \end{align*}

✓ Sympy. Time used: 0.352 (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): -4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \sqrt {18 - 2 \cos {\left (x \right )}} \]