Question

Solve the initial value problem d y d x = 2 x 1 , y ( 0 ) = 2

Answer 1

Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.

What is separation of variables?

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is given by:

$\frac{dy}{dx} = 2x$

Then, applying separation of variables:

$dy = 2x dx$

$\int dy = \int 2x dx$

$y = x^2 + K$

Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:

y(x) = x² + 2.

More can be learned about separation of variables at brainly.com/question/14318343