Solve the differential equation. . .

[tarynt1]

Solve the differential equation if given the initial condition that when x = 0, y = 7.

dy/dx = (x - 4) / sqrt(x^2 - 8x - 1)

I'm drawing a blank as far as what to do. Any help would be greatly appreciated. Thanks!

 

[camlax38]

Solve the differential equation if given the initial condition that when x = 0, y = 7.

dy/dx = (x - 4) / sqrt(x^2 - 8x - 1)

I'm drawing a blank as far as what to do. Any help would be greatly appreciated. Thanks!

Not sure if you have started the problem yet or if this will help.

You need to separate dy/dx so you have

dy=(x - 4) / sqrt(x^2 - 8x - 1)dx

So that means take the integral of each side, like integral dy=y

remember that the integral is antiderivative + some constant C

So to satisfy the initial conditions x=0, y=7 you would plug them into your anwser

so 7=integral{(x - 4) / sqrt(x^2 - 8x - 1)dx} + C (plug you x=0 once you take integral)

Now solve for C and you will obtain some number.
Your final anwser would be y=integral{(x - 4) / sqrt(x^2 - 8x - 1)dx} + C(but you now know C)

A hint to solve integral{(x - 4) / sqrt(x^2 - 8x - 1)dx} use a U substitution.

 

[tarynt1]

Thank you! That helped a lot.