When a and b are eliminated from the equation `xy=ae^x +be^-x`, the resulting differential equation is of (a) first order and first degree (b) first order and second degree (c) second order and first degree (d) second order and second degree

Options

A. first order and first degree
B. frist order and second degree
C. second order and first degree
D. second order and second degree

Answer

C

Explanation

Given equation is
` xy = ae^(x) -be^(-x)`
Differentiate both side w.r.t.'x'
` x(d^(2)y)/(dx^(2))+(dy)/(dx)+(dy)/(dx)=ae^(x)+be^(-x)`
` Rightarrow x (d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2)= xy ` (from (1))
Hence, this is the differential equation of second order and first degree.