Find the general solution to the differential equation (a: 4)y' = (93 - 4X3; - 4) y = y; help (formulas) Use the letter \"C\" for any constant of integration. Find the solution to the initialvalue problem = 311W me) = 4 da: 9 = y; help (formulas) Find the solution to the initial-value problem dy = 3xy(2 +y), y(0) = 9 dx y help (formulasFind an equation of the form 3/ = f(x) for a curve with mintercept 1 whose tangent line at any point (ac, y) has slope 9:56-11. y= f. A rocket, fired from rest at time t : 0, has an initial mass of mo (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, While fuel is being burned, will be given by m0 kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity 'u of the rocket will satisfy the equation mE2ckmg Where g is the acceleration due to gravity. (a) Find v(t) keeping in mind that the mass m is a function oft. \"(t) = f. m/sec (b) Suppose that the fuel accounts for 60% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [ Note: Take 9 = 9.8 m/s2 and c = 2500 m/s.] 11(60) = if, m/sec [Round to nearest whole number] A drug is administered intravenously to a patient at a rate r mg/h and is cleared from the body at a rate proportional to the amount of drug still present in the body, k, Where k > 0. (a) Set up the diEerential equation, assuming there is no drug initially present in the body. @_ dt f: i and y(0) 2 iv (b) Solve the differential equation y(t) = i, help (formulas)