75.4.27 problem 92

Internal problem ID [16729]
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 : Tuesday, January 28, 2025 at 08:25:54 PM
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*}

✓ Solution by Maple

Time used: 1.185 (sec). Leaf size: 21

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

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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