I need it asap

14. HOMEWORK (1) Check that y = $x2 + + 3 satisfies the differential equation ax = dy = x+1. (2) Check that y = sin t satisfies the differential equation ?2 = -y. (3) Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy = -2. What is f(x)? (4) A curve y = f (x) has the property that the slope of tangent to the curve at every point is reciprocal to the y value of the curve. Write down a differential equation whose solution is y = f (x). No need to solve this equation. (5) Determine the time it takes an amount of money to triple if compounded continuously at an annual rate of 12%. (6) Sketch a slope field corresponding to the equation @ = 3t -y. Then sketch the solution that passes through the point (1, 2). (7) I got a Guinness can whose temperature is 21 C. To enjoy it cold at the perfect tem- perature of 9 C, I set my refrigerator to O C. The temperature T(t) of the can at time t measured in seconds satisfies Newton's Cooling Law equation: = -.0001T. dt How long will it take for the can to cool off to 9.C? (8) A cup of tea with initial temperature of I = 85C is left in the room with a constant temperature A = 210. In one minute the tea cools down to 84C. What will be the temperature of the tea after an hour? When will the temperature of the tea be 22