What is the solution for y^'=(5y)/(2000+5t) ?

The solution for y^'=(5y)/(2000+5t) is y=400e^{c_{1}}+e^{c_{1}}t

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y^'=(5y)/(2000+5t)

y^{^{'}} = \frac{5 y}{2000 + 5 t}

y = 400 e^{c_{1}} + e^{c_{1}} t

Solution steps

y^{'} (t) = \frac{5 y}{2000 + 5 t}

Solve separable ODE:

y = 400 e^{c_{1}} + e^{c_{1}} t

y = 400 e^{c_{1}} + e^{c_{1}} t

\frac{d r}{d x} = \frac{4}{3} π r^{3}

\frac{d y}{d x} = 5 x^{2} y - 9 x y

x y^{^{'}} + y - 6 = 0

y^{^{'}} = \frac{x ^{2} - 5}{y ^{2}}, y (0) = 3

x^{^{'}} = (x)^{22} (ln (t) + (10) + t e^{t})

What is the solution for y^'=(5y)/(2000+5t) ?
The solution for y^'=(5y)/(2000+5t) is y=400e^{c_{1}}+e^{c_{1}}t