What is the solution for (dy)/(dx)=2sec^2(x)e^{2y},y(0)=0 ?

The solution for (dy)/(dx)=2sec^2(x)e^{2y},y(0)=0 is y=-(ln(-4tan(x)+1))/2

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(dy)/(dx)=2sec^2(x)e^{2y},y(0)=0

\frac{d y}{d x} = 2 sec^{2} (x) e^{2 y}, y (0) = 0

y = - \frac{ln ( - 4 tan ( x ) + 1 )}{2}

Solution steps

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

Solve separable ODE:

y = - \frac{ln ( - 4 tan ( x ) + 1 )}{2}

y = - \frac{ln ( - 4 tan ( x ) + 1 )}{2}

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y^{^{''}} + 4 y^{^{'}} + 8 y = 4 cos (2 t) + 2 sin (2 t)

\frac{d}{d x} (\frac{x ^{8}}{8 ( 1 - x ^{2} ) ^{4}})

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What is the solution for (dy)/(dx)=2sec^2(x)e^{2y},y(0)=0 ?
The solution for (dy)/(dx)=2sec^2(x)e^{2y},y(0)=0 is y=-(ln(-4tan(x)+1))/2