My Notes Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. (Enter your answer using interval notation.)t(t−4)y"+3ty'+4y=2,y(3)=0 ,y'(3)=−1

The answer to the question is

The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is  (-∞, 4)

Step-by-step explanation:

To apply look for the interval, we divide the ordinary differential equation by (t-4) to

y'' + y' + y =

Using theorem 3.2.1 we have p(t) =  , q(t) =  , g(t) =

Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: