75.4.28 problem 93

Internal problem ID [16730]
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 : 93
Date solved : Tuesday, January 28, 2025 at 08:25:57 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\infty \right )&=\frac {10 \pi }{3} \end{align*}

✓ Solution by Maple

Time used: 0.681 (sec). Leaf size: 23

dsolve([x^2*diff(y(x),x)+cos(2*y(x))=1,y(infinity) = 10/3*Pi],y(x), singsol=all)
 

\[ y = \frac {7 \pi }{2}-\arctan \left (\frac {\sqrt {3}\, x +6}{3 x}\right ) \]

✗ Solution by Mathematica

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

DSolve[{x^2*D[y[x],x]+Cos[2*y[x]]==1,{y[Infinity]==10/3*Pi}},y[x],x,IncludeSingularSolutions -> True]
 

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