Form the differential equation corresponding to y 2 = a(b x 2 ) by eliminating a and b.

Q6 of 462 Page 22

Form the differential equation corresponding to y² = a(b – x²) by eliminating a and b.

Given equation y² = a(b – x²)

On differentiating with respect to x, we get,

Again, differentiating with respect to x we get,

From (1) we have

On putting, this value in (2) we get,

So, the required differential equation is .

Form the differential equation of the family of curves y = Ae^2x + Be^–2x, where A and B are arbitrary constants.

Form the differential equation of the family of curves,

x = A cos nt + B sin nt, where A and B are arbitrary constant.

Form the differential equation corresponding to y² – 2 ay + x² = a² by eliminating a.

Form the differential equation corresponding to (x – a)² + (y – b)² = r² by eliminating a and b.