form the differential equation of ax2 + by2 = 1 where a and b are the arbitary constants - Maths - Differential Equations

Question

form the differential equation of ax2 + by2 = 1 where a and b
are the arbitary constants

Manbar Singh · Accepted Answer

The given equation is,ax2 + by2 = 1    
1differentiating 1 with respect to x, we get    2ax + 2bydydx = 0⇒ax = -bydydx       
2Differentiating 2 with respect to x, we geta = -by × d2ydx2 + dydx × dydx⇒a = -byd2ydx2 + dydx2   
3Dividing 2 by 3, we getaxa = -bydydx-byd2ydx2 + dydx2⇒x = ydydxyd2ydx2 + dydx2⇒xyd2ydx2 + xdydx2 - ydydx = 0This is the required differential equation