What is the solution for (dy)/(dx)=(cos(5x))/(e^{5y)} ?

The solution for (dy)/(dx)=(cos(5x))/(e^{5y)} is y=(ln(sin(5x)+c_{1}))/5

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(dy)/(dx)=(cos(5x))/(e^{5y)}

\frac{d y}{d x} = \frac{cos ( 5 x )}{e ^{5 y}}

y = \frac{ln ( sin ( 5 x ) + c _{1} )}{5}

Solution steps

\frac{d y}{d x} = \frac{cos ( 5 x )}{e ^{5 y}}

Solve separable ODE:

y = \frac{ln ( sin ( 5 x ) + c _{1} )}{5}

y = \frac{ln ( sin ( 5 x ) + c _{1} )}{5}

\int \frac{2 e ^{2 x}}{1 + e ^{2 x}} d x

y \frac{d y}{d x} = 2 x (64 + y^{2})

\frac{d}{d x} (- \frac{3 x}{y})

x \to - 2 + lim (\frac{x}{x ^{2} - 4})

3 x^{2} + 4 x + 1

What is the solution for (dy)/(dx)=(cos(5x))/(e^{5y)} ?
The solution for (dy)/(dx)=(cos(5x))/(e^{5y)} is y=(ln(sin(5x)+c_{1}))/5