What is the solution for (dy}{dx}=\frac{2(5-y))/x ?

The solution for (dy}{dx}=\frac{2(5-y))/x is y=-(c_{1})/(x^2)+5

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(dy}{dx}=\frac{2(5-y))/x

\frac{d y}{d x} = \frac{2 ( 5 - y )}{x}

y = - \frac{c _{1}}{x ^{2}} + 5

Solution steps

\frac{d y}{d x} = \frac{2 ( 5 - y )}{x}

Solve separable ODE:

y = - \frac{c _{1}}{x ^{2}} + 5

y = - \frac{c _{1}}{x ^{2}} + 5

x y^{3} d x - (y + 1) e^{- x} d y = 0

(1 + x^{2}) y^{^{'}} = - 4 x y

1 = \frac{cos ( y )}{x ^{2} sin ( y )} \frac{d y}{d x}, sin (y) > 0

x^{2} y^{^{'}} = y

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

What is the solution for (dy}{dx}=\frac{2(5-y))/x ?
The solution for (dy}{dx}=\frac{2(5-y))/x is y=-(c_{1})/(x^2)+5