I Need problems 1,2,4,5 onlyProblems 1-3 regard separable differential equations (see section 9.3) and problems 4-5 regard exponential growth and decay (see section 6.5).Solve the differential equation: dydt=tety1y22.Solve the differential equation: dzdte'**z=0.A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5galmin and the mixture is pumped out at the same rate. What is the percentage of alcohol after one hour.A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of this curve ?(a) A cup of coffee has temperature 95C and takes 30 minutes to cool to 61C in a room with temperature 20C. Show that the temperature of the coffee after t minutes is T(t)=2075(4175)(t30).(b) What is the average temperature of the coffee during the first half hour?Recall: The average value of the function T on the interval a,b is given by:Targ=1b-a*abT(t)dt