Assignment:
Q1. Find the solution of the differential equation dy/dx=x^3 -x
with the initial condition y(0) = -3.
Q2. Find the solution of the differential equation dy/dt=t^2 / (3y^2)
with the initial condition y(0) = 8.
Q3. Find the solution of the differential equation dy/dx=(x=2)y^(1/2)
with the initial condition y(0) = 1.
Q4. Find the derivative of the function f(x) = ln(x + 1)/ln(2x + 1)
Q5. Evaluate the following indefinite integral:
∫ ex eex dx =
Q6. Evaluate the following expression: sec(arctan(10))
Q7. Find the derivative of the function
f(x) = arccot(tan(2x + 3))
Provide complete and step by step solution for the question and show calculations and use formulas.