What is the solution for (dy)/(dx)=2ysqrt(16-x^2),y(0)=1 ?

The solution for (dy)/(dx)=2ysqrt(16-x^2),y(0)=1 is y=e^{16(arcsin(x/4)+1/2 sin(2arcsin(x/4)))}

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(dy)/(dx)=2ysqrt(16-x^2),y(0)=1

\frac{d y}{d x} = 2 y 16 - x^{2}, y (0) = 1

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

Solution steps

\frac{d y}{d x} = 2 y 16 - x^{2}

Solve separable ODE:

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

\frac{d}{d x} (ln (16 - x^{2}))

\int 2 (2 + x^{2})^{\frac{3}{2}} d x

\int x^{2} (x^{3} + 6)^{6} d x

f (x) = 1 + x^{3}, at x = 2

\frac{d y}{d x} = x - 1

What is the solution for (dy)/(dx)=2ysqrt(16-x^2),y(0)=1 ?
The solution for (dy)/(dx)=2ysqrt(16-x^2),y(0)=1 is y=e^{16(arcsin(x/4)+1/2 sin(2arcsin(x/4)))}