What is the solution for y^'=e^{5y}sin(6x) ?

The solution for y^'=e^{5y}sin(6x) is y=-(ln(5/6 cos(6x)-c_{1}))/5

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y^'=e^{5y}sin(6x)

y^{^{'}} = e^{5 y} sin (6 x)

y = - \frac{ln ( \frac{5}{6} cos ( 6 x ) - c _{1} )}{5}

Solution steps

y^{'} (x) = e^{5 y} sin (6 x)

Solve separable ODE:

y = - \frac{ln ( \frac{5}{6} cos ( 6 x ) - c _{1} )}{5}

y = - \frac{ln ( \frac{5}{6} cos ( 6 x ) - c _{1} )}{5}

x y^{^{'}} - 10 y = 0

\frac{d}{d x} (tan (x^{6}))

x \to 0 lim (\frac{- 6 + x}{x ^{4}})

x \to - 5 lim (\frac{x ^{2} - 7}{5 - x})

\int x (ln (x)) d x

What is the solution for y^'=e^{5y}sin(6x) ?
The solution for y^'=e^{5y}sin(6x) is y=-(ln(5/6 cos(6x)-c_{1}))/5