What is the differential equation obtained by removing the arbitrary constants in the equation $y^2=a(b^2-x^2)$?
Answer & explanation
Correct answer: option 2
Differentiating w.r.to x we get $yy'=-ax$. Differentiating again w.r.to x we get $yy''+(y')^2=-a$. Dividing the second by first we get $\frac{(y')^2+yy''}{yy'}=\frac{-a}{-ax}$. Hence we get $xyy''+x(y')^2-yy'=0$