69.4.29 problem 94

Internal problem ID [18018]
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 : 94
Date solved : Saturday, October 04, 2025 at 05:34:24 PM
CAS classification : [_separable]

\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=5 \pi \\ \end{align*}

✗ Maple

ode:=x^3*diff(y(x),x)-sin(y(x)) = 1; 
ic:=[y(infinity) = 5*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^3*D[y[x],x]-Sin[y[x]]==1; 
ic={y[Infinity]==5*Pi}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x) - sin(y(x)) - 1,0) 
ics = {y(oo): 5*pi} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions