1. The problem statement, all variables and given/known data dx/dt=x^2+1/25, and find the particular solution satisfying the initial condition x(0)=8. 2. Relevant equations 3. 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.