What is the solution for y^'=e^{2y}sin(3x) ?

The solution for y^'=e^{2y}sin(3x) is y=-(ln(2/3 cos(3x)-c_{1}))/2

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y^'=e^{2y}sin(3x)

y^{^{'}} = e^{2 y} sin (3 x)

y = - \frac{ln ( \frac{2}{3} cos ( 3 x ) - c _{1} )}{2}

Solution steps

y^{'} (x) = e^{2 y} sin (3 x)

Solve separable ODE:

y = - \frac{ln ( \frac{2}{3} cos ( 3 x ) - c _{1} )}{2}

y = - \frac{ln ( \frac{2}{3} cos ( 3 x ) - c _{1} )}{2}

y^{^{'}} = \frac{3 sec ( y )}{( x + 1 ) ^{2}}

\int (3 x - 1 x - 7 e x + 14 e) d x

\int cos^{2} (\frac{x}{2}) d x

x \to 3 lim (2 x^{2} - 7 x + 6)

\frac{d}{d x} (\frac{n}{x + 1})

What is the solution for y^'=e^{2y}sin(3x) ?
The solution for y^'=e^{2y}sin(3x) is y=-(ln(2/3 cos(3x)-c_{1}))/2