What is the solution for f(x)=3sin(5x)f^'(x)((4pi))/(15) ?

The solution for f(x)=3sin(5x)f^'(x)((4pi))/(15) is f(x)=c_{1}tan^{1/(4pi)}((5x)/2)

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f(x)=3sin(5x)f^'(x)((4pi))/(15)

f (x) = 3 sin (5 x) f^{^{'}} (x) \frac{( 4 π )}{15}

f (x) = c_{1} tan^{\frac{1}{4 π}} (\frac{5 x}{2})

Solution steps

f (x) = 3 sin (5 x) f^{'} (x) \frac{( 4 π )}{15}

Solve separable ODE:

f (x) = c_{1} tan^{\frac{1}{4 π}} (\frac{5 x}{2})

f (x) = c_{1} tan^{\frac{1}{4 π}} (\frac{5 x}{2})

y^{^{'}} = \frac{x ( x ^{2} + 1 )}{( 4 y ^{2} )}

y^{^{'}} = \frac{x ^{2}}{y ^{2}}, y (1) = 1

\frac{d x}{d t} = \frac{100 - x}{10}

(\frac{df}{d y}) f (y) = e^{- y}

4 y^{3} \frac{d y}{d x} - 5 x^{2} + 3 x = 0

What is the solution for f(x)=3sin(5x)f^'(x)((4pi))/(15) ?
The solution for f(x)=3sin(5x)f^'(x)((4pi))/(15) is f(x)=c_{1}tan^{1/(4pi)}((5x)/2)