Questions from Calculus

Q: Solve the differential equation. y2y’ = 4t3 - 3t2 +

Solve the differential equation. y2y’ = 4t3 - 3t2 + 2

Q: Solve the differential equation. y’ / (t + 1

Solve the differential equation. y’ / (t + 1) = y + 1

Q: Solve the differential equation. y’ = y/t -

Solve the differential equation. y’ = y/t - 3y, t > 0

Q: Show that the function f (t) = 3/2

Show that the function f (t) = 3/2 et2 – ½ is a solution of the differential equation y’ - 2ty = t.

Q: Show that the function f (t) = t2 – ½

Show that the function f (t) = t2 – ½ is a solution of the differential equation (y’)2 - 4y = 2.

Q: Show that the function f (t) = 5 e2t satisfies

Show that the function f (t) = 5 e2t satisfies y’’ - 3y’ + 2y = 0, y(0) = 5, y’(0) = 10.

Q: Show that the function f (t) = (e-

Show that the function f (t) = (e-t + 1)-1 satisfies y’ + y2 = y, y(0) = ½.

Q: Let t represent the total number of hours that a truck driver

Let t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p(t) represent the probability that the driver will have...

Q: State the order of the differential equation and verify that the given

State the order of the differential equation and verify that the given function is a solution. (1 - t2)y’’ - 2ty’ + 6y = 0, y(t) = ½ (3t2 - 1)

Q: Is the constant function f (t) = 3 a solution

Is the constant function f (t) = 3 a solution of the differential equation y’ = 6 - 2y?