non-linear ODE

Question 3 : 10 points Consider the Bernoulli equation: t'y' + 2e = 3'31 y(0)=1- (a) (5 points) Find the general solutions of the above differential equation. (b) (5 points) Provide a plot of the general solution[Use Python, Matlab or any software of your choice to generate your plot.) Page 2 of 3 Deoms Assignment #1 2021/08/16 Question 4 : 10 points Consider the dierential equation: r=e)'=4e)'+mo\")~w (a) (5 points) Show that the dierential equation above simplies to the Clairant's equation 2 =t :l: v Q Q (hint: Q = e) (b) (5 points) Hnoe determine the general solution and singular solution for the equation above? Question 5 : 15 points Suppose we have a tank that contains 250 gallons of water, in which there is 00 pounds of salt. Liquid is pouring into the tank at a concentration of 4 pounds per gallon, and at a rate of 4 gallons per minute. The well mixed solution leaves the tank at a rate of 5 gallons per minute. (a) (5 points) Construct an Ordinary di'erential equation that. describes the above problem. (b) (10 points) Determine the general solution to the DE in (a) using the initial value, 62(0) = '70