Determine order and degree(if defined) of differential equation (ym)2 + (yn)3 + (y')4 + y5 =0
(ym)2 + (yn)3 + (y')4 + y5 =0
The highest order derivative present in the differential equation isym. Therefore, its order is three.
The given differential equation is a polynomial equation in ym , yn , y'.
The highest power raised to ym is 2. Hence, its degree is 2.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by , where R+ is the set of all non-negative real numbers.
y = Ax : xy' = y (x ≠ 0)