What is the solution for sqrt(1-7x^2)(dy)/(dx)=x ?

The solution for sqrt(1-7x^2)(dy)/(dx)=x is y=-1/7 sqrt(1-7x^2)+c_{1}

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sqrt(1-7x^2)(dy)/(dx)=x

1 - 7 x^{2} \frac{d y}{d x} = x

y = - \frac{1}{7} 1 - 7 x^{2} + c_{1}

Solution steps

1 - 7 x^{2} \frac{d y}{d x} = x

Substitute

\frac{d y}{d x}

with

y^{'} (x)

1 - 7 x^{2} y^{^{'}} (x) = x

Isolate

y^{'} (x) : y^{'} (x) = \frac{x}{1 - 7 x ^{2}}

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

then

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

y = \int \frac{x}{1 - 7 x ^{2}} d x

\int \frac{x}{1 - 7 x ^{2}} d x = - \frac{1}{7} 1 - 7 x^{2} + c_{1}

y = - \frac{1}{7} 1 - 7 x^{2} + c_{1}

(2 x y^{4} - 2 x y) d x - (3 + 3 x^{2}) d y = 0

x \to 1 lim (\frac{x ^{2} - x}{x - 1})

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

\frac{\partial}{\partial y} (\frac{2 y}{( x + y ) ^{2}})

7 e^{x}

What is the solution for sqrt(1-7x^2)(dy)/(dx)=x ?
The solution for sqrt(1-7x^2)(dy)/(dx)=x is y=-1/7 sqrt(1-7x^2)+c_{1}