73.7.40 problem 40

Internal problem ID [15127]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 40
Date solved : Monday, March 31, 2025 at 01:26:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.220 (sec). Leaf size: 10

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

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