A. Solve the following initial value problem: \\[\\cos(t)^2 \\frac{dy}{dt} = 1\\
ID: 1949196 • Letter: A
Question
A. Solve the following initial value problem: [cos(t)^2 rac{dy}{dt} = 1] with (y( 17 ) = an(17)).
(Find (y) as a function of (t).)
(y =) .
B. On what interval is the solution valid?
(Your answer should involve pi.)
Answer: It is valid for (< t <) .
C. Find the limit of the solution as (t) approaches the left end of the interval. (Your answer should be a number or "PINF" or "MINF".
"PINF" stands for plus infinity and "MINF" stands for minus infinity.)
Answer: .
D. Similar to C, but for the right end.
Answer: .
Explanation / Answer
A. dy = dt=cos^2t Integrating, y = tant + c y(17) = tan17 => tan17 = tan17 + c => c = 0 So, y = tant B. It is valid for R-{...., -3pi/2, -pi/2, pi/2, 3pi/2....} C. y = MINF D. y = PINF