Answer to Question #50668 in Differential Equations for Nikhil

Question

1. Classify the following statements as true or false giving reasons for your answers.

i) y = 0 , is the singular solution of the differential equation 27y - 8(dy/dx)^3 =0.

ii) The differential equation corresponding to the equation y = cx^2 + 1 is (dy/dx) - (2y/x) = -(2/x).

iii) y' + P(x) y = Q(x) y^n is a linear equation for integral values of n.

iv) PDE u (du/dx) = e^y sin x, u = u(x, y) is a quasi-linear p.d.e.

v) The differential equation
t(d^2z/dx^2)+2(d^2z/dxdt)+x(d^2z/dt^2)+(dz/dx)=0
is elliptic if xt <1.