Question

What is the solution to the differential equation dydx=5y2 with the initial condition y(0) = 3?

Answer 1

Answer:

Step-by-step explanation:

$dydx = 5y^{2} \\\frac{dy}{5y^{2}} = dx$

Integrating both sides yields:

$-\frac{1}{5y} = x + c\\ y = -\frac{1}{5x + 5c} \\y(0) = 3 => 3 = -\frac{1}{0 + 5c} => c = -\frac{1}{15}$

Our solution is:

$y = -\frac{1}{5x - \frac{1}{3} }$