A tank initially contains 100 gallons of brine in which 40

Question

Solve differential equation

1. 2x dx/dy + y = 3x⁴

2.(x+6) dy/dx + y = x² - 36

3. dy/dx - y/x = (Ln x)²

Slove the differential equation subject to the initial condition.

1. 2 dy/dx - 4xy = 8x

A tank initially contains 100 gallons of brine in which 40 pounds of salt was dissolved. a brine containing 2 lb/gal of salt runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gallons per minute find the solution to the differential equation that models the mixing process.

Find the exact value of the real number y.

1. y= csc^-1 (1)
2. y= arcsin (-1/2)