Question

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

Answer 1

Differential equation is a way to represents the relation between the functions and their variables. The solution to the differential equation given in the question is,

$y=\dfrac{3}{15x-1}$

Given-

The equation in the question is,

${dy\times {dx}=5y^2$

What is differential equation?

Differential equation is a way to represents the relation between the functions and their variables.

Rewrite the equation,

$\dfrac{dy}{5y^2} =dx$

Integration both sides,

$-\dfrac{1}{5y} =x+c$

Here, c is the integrating constant.

Now the given initial condition is,

$y(0)=3$

Use this for the integrated function to find the value of the constant,

$-\dfrac{1}{5\times 3} =c$

$c=-\dfrac{1}{15}$

Put this value in equation we get,

$-\dfrac{1}{5y} =x-\dfrac{1}{15}$

$y=\dfrac{3}{15x-1}$

Hence the solution to the differential equation given in the question is,$y=\dfrac{3}{15x-1}$

For more about the differential equation follow the link below-https://brainly.com/question/25731911