Write step-by-step solutions and justify your answers. Solve the following questions using the methods discussed in Sections 2.2, 2.3, and 2.4. 1) [20 Points] Consider the DE: 15x²y + 3x³y' - 24y = 0. A) Solve the given differential equation by separation of variables. B) Find a solution that satisfies the initial condition y(1) = 1. 2) [20 Points] A) Solve the IVP: (2x - 4) - 2 In 5x + 2y = 0, y(3) = 3. dy dx B) Give the largest interval over which the solution is defined. 3) [20 Points] Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is exact. B) Solve the differential equation.