The differential equation of the ellipse x^2/a^2 + y^2/b^2 = C is

Question

The differential equation of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=C\) is

A. \(\frac{y''}{y'}+\frac{y'}{y}-\frac{1}{x}=0\)

B. \(\frac{y''}{y'}+\frac{y'}{y}+\frac{1}{x}=0\)

C. \(\frac{y''}{y'}-\frac{y'}{y}-\frac{1}{x}=0\)

D. None of these

Answer 1

Correct answer is A.

x²/a² + y²/b² = C

Since the equation has 2 constants so we differentiate twice,

Differentiating w.r.t x

Again, differentiating w.r.t x

Substitute value of (2) in (1) we get,

Dividing both sides by y.y’ we get,