Question

Classify the following statements as true or false giving reasons for your answers.  i) General solution of the differential equations x^2(d^2y/dx^2)^(3) +y(dy/dx)^(4) +y^4 =0 must  contain four arbitrary constants.

(ii) The set of real (or complex) solutions of equation y'(x) + P(x)y(x)=Q(x) fo

Answer 1

I) False. The order of this equation is 2, hence it should contain 2 arbitraty constants

II) True. For all$\lambda, \mu\in C λ,μ∈C$  If $y_1$ ​and $y_2$ ​ are solutions of the equation,$\lambda y_1+\mu y_2$  is also the solution.