40.4.21 problem 23 (a)

Internal problem ID [6661]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 23 (a)
Date solved : Sunday, March 30, 2025 at 11:15:20 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }&=2 x \sin \left (y\right )-1 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

ode:=x^2*cos(y(x))*diff(y(x),x) = 2*x*sin(y(x))-1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\arcsin \left (\frac {3 c_1 \,x^{3}-1}{3 x}\right ) \]

✓ Mathematica. Time used: 10.037 (sec). Leaf size: 21

ode=x^2*Cos[y[x]]*D[y[x],x]==2*x*Sin[y[x]]-1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \arcsin \left (\frac {1}{3 x}+2 c_1 x^2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*cos(y(x))*Derivative(y(x), x) - 2*x*sin(y(x)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x*sin(y(x)) - 1)/(x**2*cos(y(x))) cannot be solved by the factorable group method