Solving ODE w/ Initial Condition: Verify & Determine Particular Solution

[ombudsmansect]

ODE solutions :(

hey guys, I am attempting to prove this:

Verify that y is a solution of the ODE. Determine from y the particular solution satisfying the given initial condition.

y' = 1 + 36y^2 , y = (1/6)tan(6x+c) y(0) = 0

It can be seen that it is a solution

I then calculate that the particular solution for the specified point is:

y = 1/6tan6x


Can anyone see where I am going wrong here?
The program says this is not correct. I would assume c = tan^-1 0 and that follows. thanks for all help

 

[HallsofIvy]

Yes, y= (1/6)tan(6x) is correct. But "programs" are notorious for insisting that an answer be in exactly the right form. If you wrote 1/6tan6x without parentheses, it may be interpreting it as 1/(6 tan(6x)) which would be wrong. Or it could be asking you for the value of c so that "0" is the correct answer.

 

[ombudsmansect]

Thanks HallofIvy,

Turns out it was correct, it was a multiple choice question and it turns out the program was so wrong it didnt even have the answer listed. Cheers