separatable first order differential equation question Pleas

separatable first order differential equation question. Please solve step-by-step, thank you.

Solve the separable differential equation dx/dt= x^2+f1/16 and find the particular solution satisfying the initial condition x(0)=7.

dx/dt = x^2 + 1/16

Now separate the terms :

dx/( x^2 +1/16) = dt

Now integrate both sides:

4arctan(4x) = t +c where c is constant

Now find c uing x(0) =7

So, 4arctan(28) = 0 +c

c= 4arctan(28)

So, 4arctan(4x) = t +c

arctan4x = (t+c)/4

x= (1/4)tan(t+c)/4

x= (1/4) tan ( 4arctan28) +t)/4