75.4.30 problem 95

Internal problem ID [16732]
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 : 95
Date solved : Tuesday, January 28, 2025 at 09:19:52 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-\infty \right )&=\frac {7 \pi }{2} \end{align*}

✓ Solution by Maple

Time used: 1.427 (sec). Leaf size: 17

dsolve([(1+x^2)*diff(y(x),x)-1/2*cos(2*y(x))^2=0,y(-infinity) = 7/2*Pi],y(x), singsol=all)
 

\[ y = \frac {\arctan \left (\arctan \left (x \right )+\frac {\pi }{2}\right )}{2}+\frac {7 \pi }{2} \]

✗ Solution by Mathematica

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

DSolve[{(1+x^2)*D[y[x],x]-1/2*Cos[2*y[x]]^2==0,{y[-Infinity]==7/2*Pi}},y[x],x,IncludeSingularSolutions -> True]
 

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