Question

Entered Answer Preview Result Message incorrect The domain of your function doesn't match that of the correct answer 2 correct 10 10 correct infinite infinite correct 0 correct At least one of the answers above is NOT correct. (1 point) A. Solve the following initial value problem: (<? - 121 +20) 4x- y dy dt with y(6) 1. (Find y as a function of t.) y(t-10) (t-2)(1/10) B. On what interval is the solution valid? Answer: It is valid for 2 <t<10 C. Find the limit of the solution as t approaches the left end of the interval (Your answer should be a number or the word "infinite".) Answer: infinite D. Similar to C, but for the right end Answer: 0

Answer 1

Given (t^2 - 12t + 20) dy/dt = y dy/y = dt/(t^2 - 12t + 20) dy/y = dt/(t - 10) (t - 2) dy/dt = dt [1/8/t - 10 + -1/8/t - 2] dy/dt = 1/8 [dt/t - 10 - dt/t - 2] Now Integrate integral dy/y = 1/8 [integral dt/t - 10 - integral dt/t - 2] ln y = 1/8 [ln (t - 10) - ln (t - 2)] + c ln y = 1/8 [ln (t - 10/t - 2)] + c ln y = ln [t - 10/t - 2]^1/8 + ln k (Because c = ln k) ln y = ln [t - 10/t - 2]^1/8 K \r\n Therefore y = K [t - 10/t - 2]^1/8 given y(6) = 1 1 = K[6 - 10/6 - 2]^1/8 1 = K [-4/4]61/8 1 = K[-1]^1/8 K = 1 Therefore y = [t - 10/t - 2]^1/8