What is the solution for (dy)/(dx)=4x+(4x)/(sqrt(16-x^2)) ?

The solution for (dy)/(dx)=4x+(4x)/(sqrt(16-x^2)) is y=2x^2-4sqrt(16-x^2)+c_{1}

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(dy)/(dx)=4x+(4x)/(sqrt(16-x^2))

\frac{d y}{d x} = 4 x + \frac{4 x}{16 - x ^{2}}

y = 2 x^{2} - 4 16 - x^{2} + c_{1}

Solution steps

\frac{d y}{d x} = 4 x + \frac{4 x}{16 - x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 4 x + \frac{4 x}{16 - x ^{2}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 4 x + \frac{4 x}{16 - x ^{2}} d x

\int 4 x + \frac{4 x}{16 - x ^{2}} d x = 2 x^{2} - 4 16 - x^{2} + c_{1}

y = 2 x^{2} - 4 16 - x^{2} + c_{1}

x \to 8 lim (\frac{3 x ^{2}}{4})

\int \frac{x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 3 y = 65 sin (2 t)

f (x) = 3 - x

x^{2} + 1, x, [0, 1]

What is the solution for (dy)/(dx)=4x+(4x)/(sqrt(16-x^2)) ?
The solution for (dy)/(dx)=4x+(4x)/(sqrt(16-x^2)) is y=2x^2-4sqrt(16-x^2)+c_{1}