Question and answers are shown. But I cannot understnad how did it set there.

So, please provide step by step solution for each question. Please solve it, I experienced some tutors just explain without any solution.

1. Separation of variable

Find the general solution of the given differential equation 477y =y + dzeV. (Use C as an arbitrary constant of integration). y = In((4*In(abs(4*x\"2-1))+C)/8) Find the particular solution of the equation. +2 dy dt ty = 0, y (6) = 7, t>0 y =7*e^(1/t-1/6)A 400-gallon tank initially contains 200 gallons of brine containing 75 pounds of dissolved salt. Brine containing 3 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon per minute. Set up a differential equation for the amount of salt, A(t), in the tank at time . (Use "A" for any "A(t)" needed in the equation) dA il 12-A/(3*t+200) Find a power series representation for the following function and the radius of convergence. f ( x) = 10x + 15 E 15^((-n)-1)*(-1)^n*10^n*x^(n+1) 2=0 Computer's answer now shown above. Incorrect. Tries 7/99 Previous Tries Radius of Convergence: R = 3/2 Computer's answer now shown above. You are correct. Your receipt no. is 151-7267 (? Previous Tries. | Find the integrating factor for the following differential equation (cos8z)y' 8(tan8z)y = 2sec8z, 0O0