75.4.34 problem 99

Internal problem ID [16665]
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 : 99
Date solved : Monday, March 31, 2025 at 03:04:13 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\infty \right )&=\frac {11 \pi }{4} \end{align*}

✓ Maple. Time used: 0.177 (sec). Leaf size: 20

ode:=x^2*diff(y(x),x)+sin(2*y(x)) = 1; 
ic:=y(infinity) = 11/4*Pi; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\arctan \left (\frac {x +2}{x -2}\right )+3 \pi \]

✗ Mathematica

ode=x^2*D[y[x],x]+Sin[2*y[x]]==1; 
ic={y[Infinity]==11/4*Pi}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.357 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + sin(2*y(x)) - 1,0) 
ics = {y(oo): 11*pi/4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {atan}{\left (\frac {1}{1 - x} \right )} \]