Proving a formula is a solution

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Posted by Diana on November 04, 2002 at 18:36:00:

I am trying to verify that the given formula is a solution to the initial value problem.

Y'=y^3
y(0) = 5
Formula: y(t) = 1 / sqrt(1/25-2t)

I know that 1/sqrt(1/25-2t) at y(0) = 5

When I try to differentiate this, though, I run into problems.

-(sqrt 1/25-2t)^-2* [(1/25-2t)^-1/2]/2 * 2
Since the twos cancel, I end up with
-(sqrt 1/25-2t)^-2* [(1/25-2t)^-1/2]

That can't be right since I am sure this formula is a solution - just looking at the problems that follow this. What have I done wrong?



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