Q1) Solve the differential equation

(y^(13) x )(dy)/(dx) = 1 + x.

use the initial condition y(1)=3 , express y^14 in terms of x

Q2) find the function y=y(x) for x>0

(dy)/(dx) = (2 + 12 x)/(xy^2) x > 0

y(1)=2 y?

Q3) (dy)/(dx) = 4 y , y(0)=-1 find y(x)

Q4) (dx)/(dt) = x^2 + (1)/(49) , find particular solution satisfying the initial condition x(0)=3 find x(t)

Q5) Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $80000 in the account. Each year the account earns 5% interest, and you deposit $8000 into the account. (dy)/(dt) = 0.05 y + 8000

y(0)=80000

find y(t)

Q6)

Let y(t) represent your retirement account balance, in dollars, after t years. Each year the account earns 8% interest, and you deposit 6% of your annual income. Your current annual income is $38000, but it is growing at a continuous rate of 4% per year.

write the differential equation modeling this situation dy/dt=

Q7) The liquid base of an ice cream has an initial temperature of 91C before it is placed in a freezer with a constant temperature of -16C. After 1 hour, the temperature of the ice-cream base has decreased to 65C. Use Newton's law of cooling to formulate and solve the initial-value problem to determine the temperature of the ice cream 2 hours after it was placed in the freezer. Round your answer to two decimal places.

Q8) A tank contains 100 kg of salt and 1000 L of water. A solution of a concentration 0.5 kg of salt per liter enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the same rate.

a. Find the amount of salt in the tank after 2.5 hours. amount

b. Find the concentration of salt in the solution in the tank as time approaches infinity. concentration