SOLUTION: Find a solution to the initial value problem y′+sin(t)y=g(t), y(0)=7, g(t)= −sin(t),if π < t ≤ 2π. y(t)=___________ _

SOLUTION: Find a solution to the initial value problem y′+sin(t)y=g(t), y(0)=7, g(t)= −sin(t),if π < t ≤ 2π. y(t)=_________ ,if π < t ≤ 2π.

Question 1184451: Find a solution to the initial value problem
y′+sin(t)y=g(t), y(0)=7, g(t)= −sin(t),if π < t ≤ 2π.
y(t)=______________,if π < t ≤ 2π.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

I have my doubts on your function g(t), as it is defined on π < t ≤ 2π, but your IVP starts at t = 0,
so there is a bit of an incompatibility between the solution function y(t) and g(t).

If we still push ahead with the solution, the integrating factor is .

This then implies , or .

Plugging in y(0) = 7, and solving for C, you should get , for π < t ≤ 2π.

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SOLUTION: Find a solution to the initial value problem y′+sin(t)y=g(t), y(0)=7, g(t)= −sin(t),if π < t ≤ 2π. y(t)=___________ __,if π < t ≤ 2π.

SOLUTION: Find a solution to the initial value problem y′+sin(t)y=g(t), y(0)=7, g(t)= −sin(t),if π < t ≤ 2π. y(t)=_________ ,if π < t ≤ 2π.