Answer to Question #330263 in Differential Equations for Shraddha

Question

Solve True / False by giving reasons for your answers.

a) The integrating factor of the differential equation

xdx + ydy = m(xdy + ydx) is .

1/xy. ?

b) The equation (δ^2 z)/ ( δ^2 x) + x^2 × (( δ^2 z) / ( δ y^2)) = 0

is hyperbolic. ?

c) The solution of the differential equation

( D^3 + D^2 D' - DD'^2 - D'^3 ) is

z = θ1 ( y + x ) + θ2 ( y - x ) + x^2 θ3 (y-x ) ?

d) The Pfaffian differential equation

a^2× y^2 × z^2 dx + b^2 × z^2 × x ^2 dy + c^2 × x ^2 ×y ^2 dz = 0 is Integrable. ?

e) The general solution of the equation x ^2 × y'' + xy'- y = 0,

defined in [0,1] is given

y = c1 × x + c2 × x^-1 ?