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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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