Internal problem ID [15002]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}=0} \] With initial conditions \begin {align*} \left [y \left (-\infty \right ) = \frac {7 \pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.437 (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: 0.0 (sec). Leaf size: 0
DSolve[{(1+x^2)*y'[x]-1/2*Cos[2*y[x]]^2==0,{y[-Infinity]==7/2*Pi}},y[x],x,IncludeSingularSolutions -> True]
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