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The differential equation representing all circles in a plane is (with y1 = dy/dx, y2 = d²y/dx², y3 = d³y/dx³). Which statement is correct?

1. y3*(1 + y1²) - 3*y1*y2² = 0
2. of order 3 and degree 1
3. of order 3 and degree 2
4. y3²*(1 - y1²) - 3*y1*y2² = 0

Correct answer: y3*(1 + y1²) - 3*y1*y2² = 0

Solution

Eliminating the three constants of a general circle leads to (1 + y1²)*y3 - 3*y1*y2² = 0, an order-3, degree-1 equation.

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