To solve the differential equation

  dy/dx + 2xy=x use bernoulli therorem hint: this problem is in the form of dy/dx +p(x)y=Q(x) find integrating factor (IF) then use general formula i.e y*IF= integration of IF *Q(x)  

Solving Algebraic Problems with Quadratic Equations

  a) Show that the solutions of the equation \(x^2 – 6x – 43 = 0\) can be written in the form \(x = p \pm \frac{q\sqrt{13}}{13}\), where \(p\) and \(q\) are positive integers. b) Based on the above or any other method, solve the inequality \(x^2...