What is the solution for 2(dy}{dx}-1/y =\frac{2x)/y ?

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

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2(dy}{dx}-1/y =\frac{2x)/y

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

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

Solution steps

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

Solve separable ODE:

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

y = x^{2} + x + c_{1}, y = - x^{2} + x + c_{1}

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

y^{^{'}} + cos (x) \cdot y = 3 \cdot cos (x)

d y = \frac{y + 4}{x + 3} d x

(x^{2} + 1) d t = 4 t x \cdot d x

y^{^{'}} = - \frac{x - 8}{y - 3}, y (8) = 1

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