1. Determine the order of the below differential equations. Also, state whether the equation is linear or nonlinear. No need to explain why. d’y d²y +6y- di? a) (² +5)- + tan y = 0 dt -cos (2y+t)+r°...

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Extracted text: 1. Determine the order of the below differential equations. Also, state whether the equation is linear or nonlinear. No need to explain why. d’y d²y +6y- di? a) (² +5)- + tan y = 0 dt -cos (2y+t)+r° d´y_d*y sin(3t) dt* b) dt Determine whether y(t) = 2e – 3e' is a solution to y" +2y' – 3y = 0. Find the solution of the given initial value problem. y'-2y = ťe* 2. 3. y(0) = 5 . 4. Find the explicit result for function y (i.e. function y = an function in term of x) of the initial value 3x y' = - y+x*y problem y(0) =-4 . Verify that (e* sin y +3y)-(3x-e* sin y)y' = 0 is exact. Then solve the equation. 5. 6. A huge tank, which has capacity up to 1000 gal, contains 300 gal of water with 100 lb of salt in solution. Water containing 3 lb of salt per gallon is pouring into the tank at a rate of 4 gal/min, and the mixture is allowed to flow out of the tank at a rate of 1 gal/min. Draw out a figure to summarize the problem. Then find the amount of salt in the tank at the end of 60 minutes.