5.
a) Solve the following differential equation:
$$\frac{dy}{dx} = \frac{1+y^2}{1+x}$$
b) Consider the equation:
$$f(x, y) = 5x^4 + 2x^2 - 10xy - y^4 - 3 = 0$$
Find $$dy/dx$$ at the point (2,3).
c) By working out the Taylor series expansion of sin x centered about $$x = \pi/6$$, how many terms are required to calculate sin x to an accuracy of 0.015 for x in the range $$[0, \pi/2]$$?
