69.4.27 problem 92

Internal problem ID [18016]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 92
Date solved : Sunday, October 12, 2025 at 05:33:16 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=\frac {16 \pi }{3} \\ \end{align*}

✓ Maple. Time used: 0.194 (sec). Leaf size: 21

ode:=x^2*diff(y(x),x)*cos(y(x))+1 = 0; 
ic:=[y(infinity) = 16/3*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {\sqrt {3}\, x -2}{2 x}\right )+5 \pi \]

✗ Mathematica

ode=x^2*D[y[x],x]*Cos[y[x]]+1==0; 
ic={y[Infinity]==16/3*Pi}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*cos(y(x))*Derivative(y(x), x) + 1,0) 
ics = {y(oo): 16*pi/3} 
dsolve(ode,func=y(x),ics=ics)