Assignment:
Q1. First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4.
Q2. Solve the initial value problem dy/dx = y^3 , y(0) = 1
Q3. Find the center and radius of the circle described in the equation 2x^2+2y^2-6x+2y=3.
Q4. Find the equation of the ellipse with the center (2,1), horizontal major axis 10, and eccentricity 2/5.
Provide complete and step by step solution for the question and show calculations and use formulas.