Question

Solve the following Initial Value Theorem:
dy/dt = sec^2(t) - sin(t), y(pi/4) = 1

Answer 1

The solution to the equation is:
\[y(t) = c + \cos(t) + \tan(t) \]
Replace each t with Pi/4. The function value y(Pi/4) is one.
\[1=c+\cos{\pi \over 4} +\tan{\pi \over 4}\]
Solve for c and replace it's value in the original solution.
\[y(t)= -\frac{1}{\sqrt{2}}+\cos(t)+\tan(t) \]