Question

Consider the differential equation dydx=6x, dydx=6x, with initial condition y(0)=4y(0)=4.

Answer 1

Formatting is kind of messed up. I'm assuming the differential equations is dy/dx = 6x

You need to get all the x's on one side and y'all on the other.

dy =6x dx

Integrate both sides.

y = 3x^2 + C

Now plug in the given values

y(0) = 4 = 3(0)^2 + C

C = 0

y = 3x^2

Plug 1 in for x to find the value of y(1)

y(1) = 3(1)^2 = 3