Question

form differential equation of xy=ae^x+b^-x where ab are ordinary constants​

Answer 1

Step-by-step explanation:

x y = a e ^ { x } + b ^ { - x }

$x y = a e ^ { x } + b ^ { - x }$

$\ln x y = \ln a + x - x \ln b$

differetiate

$\frac { 1 } { x y } ( y + x y ^ { \prime } ) = 1 - \ln b$

differetiate again taking xy to rhs

$y ^ { \prime } + y ^ { \prime } + x y ^ { \prime \prime } = ( y + x y ^ { \prime } ) ( 1 - \ln b )$

now put value of (1- ln b ) from 2nd last eqn

$2 y ^ { \prime } + x y ^ { \prime \prime } = \frac { ( y + x y ^ { \prime } ) ^ { 2 } } { x y }$

this is a differential eqn of 2nd order.