Finding a Particular Solution for a Separable Equation with Initial Condition

[Temp0]

Homework Statement

dx/dt=x^2+1/25,
and find the particular solution satisfying the initial condition
x(0)=8.

Homework Equations

The Attempt at a Solution

So I began by taking out 1/25 from the right side, making the equation:
dx/dt = (1/25)(25x^2 + 1)
Then, rearranging the equation to be:
dx/(25x^2+ 1) = (1/25) dt
Taking the integral of both sides:
tan^-1(5x) = (1/25) t + c
Using the initial value x(0) = 8, I can solve for c, so first I rearrange for x.
5x = tan( (1/25)t + c)
x = tan ( (1/25)t + c)/5
Plugging in 0 and 8 into the equation gives me that c = tan^-1 (40)
However, I don't have the right answer. Can anyone help me recognize what I did wrong here? Thank you in advance.

 

[jz92wjaz]

dx/(25x^2+ 1) = (1/25) dt
Taking the integral of both sides:
tan^-1(5x) = (1/25) t + c

I see a mistake on the left hand side that you might spot if you do a u substitution. (u=5x, du=?)

 

[Temp0]

Oh, thank you, I didn't notice that. Haha, that was careless of me.