What is the solution for y^'=-(0.1y)/(0.5-0.1x) ?

The solution for y^'=-(0.1y)/(0.5-0.1x) is y=0.5e^{c_{1}}-0.1e^{c_{1}}x

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y^'=-(0.1y)/(0.5-0.1x)

y^{^{'}} = - \frac{0.1 y}{0.5 - 0.1 x}

y = 0.5 e^{c_{1}} - 0.1 e^{c_{1}} x

Solution steps

y^{'} (x) = - \frac{0.1 y}{0.5 - 0.1 x}

Solve separable ODE:

y = 0.5 e^{c_{1}} - 0.1 e^{c_{1}} x

y = 0.5 e^{c_{1}} - 0.1 e^{c_{1}} x

\frac{d N}{d t} = k (20 - N)

\frac{d y}{d t} = 0.06 y + 3000, y (0) = 70000

\frac{d y}{d x} y = u^{2} + 2 u, u = \frac{1}{x ^{2}}

d x + sin (y) x d y - sin (y) d y = 0

f^{^{'}} (x) = - 10 f (x)

What is the solution for y^'=-(0.1y)/(0.5-0.1x) ?
The solution for y^'=-(0.1y)/(0.5-0.1x) is y=0.5e^{c_{1}}-0.1e^{c_{1}}x