11. Bernuolli Differential Equations. A Bernuolli ODE is of the form y' + P(x)y = Q(x)y". (1) (a) Show that Eq (1) can be transformed into the following First-order Linear ODE by change of variable u = y-"; (b) Solve the Bernuolli ODE: du dr + (1 n)P(x)u = (1 n)Q(x). xy' + y = xy. (2) 12. Mixing problem 1. A tank contains 100 L of water. A solution with salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. (a) If y(t) is the amount of salt (in kg) after t minutes, show that y satisfied the ODE: dy dt 3y 100+2t (b) Solve the above ODE, and find the concentration after 20 minutes. (3)