What is the solution for y^'=e^{4y}(sin(5x)) ?

The solution for y^'=e^{4y}(sin(5x)) is y=-(ln(4/5 cos(5x)-c_{1}))/4

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y^'=e^{4y}(sin(5x))

y^{^{'}} = e^{4 y} (sin (5 x))

y = - \frac{ln ( \frac{4}{5} cos ( 5 x ) - c _{1} )}{4}

Solution steps

y^{'} (x) = e^{4 y} (sin (5 x))

Solve separable ODE:

y = - \frac{ln ( \frac{4}{5} cos ( 5 x ) - c _{1} )}{4}

y = - \frac{ln ( \frac{4}{5} cos ( 5 x ) - c _{1} )}{4}

\int \frac{1}{x 4 - ( ln ( x ) ) ^{2}} d x

y = 12 - x^{2}, y = - 4 x + 0, [3, 8]

\frac{d}{d x} (e^{1 + x})

\int sec (2 x) tan^{5} (2 x) d x

\int (e^{x y}) d y

What is the solution for y^'=e^{4y}(sin(5x)) ?
The solution for y^'=e^{4y}(sin(5x)) is y=-(ln(4/5 cos(5x)-c_{1}))/4