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

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

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(dy)/(dx)=e^{2y}sin(3x)

\frac{d y}{d x} = e^{2 y} sin (3 x)

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

Solution steps

\frac{d y}{d 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}

f (x) = \frac{7}{x}, at x = 1

\frac{\partial}{\partial x} ((x)^{2} y)

\int x^{2} (3 - 2 x) d x

x^{2} - 6 x, 0

\int_{\frac{π}{4}}^{\frac{π}{3}} cot (x) d x

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