Question

from the differential equation by eliminating
the arbitary constants from y² = ax+b.​

Answer 1

Answer:

Number of arbitrary constant is 1, so we may differentiate the equation once to find the differential equation.

2y(dy/dx) = 4a(1)

2y(dy/dx) = 4a

dy/dx = 4a/2y

dy/dx = 2a/y ---- (1)

By finding the value of y from equation (1), we get

y2 = 4ax

a = y2/4x

now we are going to apply the value of a in the first equation

dy/dx = 2(y²/4x)/y

dy/dx = 2y²/4xy

y' = y/2x

2xy' = y

y = 2xy'

Therefore the required equation is y = 2xy