What is the solution for (dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2)) ?

The solution for (dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2)) is y=2sin(sqrt(1+x^2)+c_{1})

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(dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2))

\frac{d y}{d x} = \frac{x 4 - y ^{2}}{1 + x ^{2}}

y = 2 sin (1 + x^{2} + c_{1})

Solution steps

\frac{d y}{d x} = \frac{x 4 - y ^{2}}{1 + x ^{2}}

Solve separable ODE:

y = 2 sin (1 + x^{2} + c_{1})

y = 2 sin (1 + x^{2} + c_{1})

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

2 x sin^{2} (y) d x - (x^{2} + 10) cos (y) d y = 0

\frac{d y}{d x} = cos (x) sin (y)

y^{^{'}} + 17 \frac{y}{x} = 0

x^{^{'}} = 1 - \frac{11}{5} x

What is the solution for (dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2)) ?
The solution for (dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2)) is y=2sin(sqrt(1+x^2)+c_{1})