Solving a Quadratic Equation with Initial Conditions

[jacko200]

Ok, the question I have is attached. What I have done is found the general solution:

(Question was seperable, so it was easy)
y = x^2 - 2x + c

But I don't kwow what/how to do is finding the initial conditions where there are:
(a) No solutions
(b) more than one solution
(c) precisely one solutions

Thanks

 

[mezarashi]

I don't see your ODE, but if that quadratic is your solution, it only takes algebra to solve the problem. Recall your quadratic equation. Your discriminant (the stuff inside the square root) will tell you about the nature of the solution. Just in case you forgot.

1) Discriminant is positive: more than one solution
2) Discriminant is zero: one solution
3) Discriminant is negative: no real solution (imaginary solutions)

Your "initial condition" is the value of "c".