What is the solution for y^'=(cos^2(x))(cos^2(6y)) ?

The solution for y^'=(cos^2(x))(cos^2(6y)) is y=(arctan(3(x+1/2 sin(2x))+c_{1}))/6+(pin)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^'=(cos^2(x))(cos^2(6y))

y^{^{'}} = (cos^{2} (x)) (cos^{2} (6 y))

y = \frac{arctan ( 3 ( x + \frac{1}{2} sin ( 2 x ) ) + c _{1} )}{6} + \frac{πn}{6}

Solution steps

y^{'} (x) = (cos^{2} (x)) (cos^{2} (6 y))

Solve separable ODE:

y = \frac{arctan ( 3 ( x + \frac{1}{2} sin ( 2 x ) ) + c _{1} )}{6} + \frac{πn}{6}

y = \frac{arctan ( 3 ( x + \frac{1}{2} sin ( 2 x ) ) + c _{1} )}{6} + \frac{πn}{6}

What is the solution for y^'=(cos^2(x))(cos^2(6y)) ?
The solution for y^'=(cos^2(x))(cos^2(6y)) is y=(arctan(3(x+1/2 sin(2x))+c_{1}))/6+(pin)/6