Question

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

c₁x³ + c₂y² = 5.

Answer 1

c₁x³ + c₂y² = 5 .....(1)

Differentiating w.r.t. x, we get

Differentiating again w.r.t. x, we get

The equations (1), (2) and (3) in c₁ , c₂ are consistent.

∴ determinant of their consistency is zero.

This is the required D.E.