Assignment:
Q1. First find a general solution of the differential equation dy/dx = 3y. Then find a particular solution that satisfies the initial condition that y(1) = 4
Q2. Solve the initial value problem dy/dx = y3 , y(0) = 1
Q3. Find the centre and radius of the circle described in the equation
2x2 + 2y2 – 6x + 2y = 3
Q4. Given a = 2 i + 3 j , b = 3 i + 5 j , and c = 8 i + 11 j express c in the form ra + sb where r and s are scalars.
Q5. Given a = < 4 , – 3 , – 1 > and b = < 1 , 4 , 6 > find a × b .
Provide complete and step by step solution for the question and show calculations and use formulas.