Class 12

Math

Calculus

Differential Equations

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.

differenciate with respect to x

$E_{′}=a_{2}2x +b_{2}2yy_{′} =0$

$b_{2}a_{2} =yy_{′}−x −(1)$

again differentiate with respect to x

$E_{′′}=a_{2}2 +b_{2}2y_{′2}+2yy_{′} =0$

$b_{2}a_{2} =y_{′2}+yy_{′}−1 −(2)$

from equation 1 and 2

$yy_{′}x =y_{′2}+2yy_{′}1 $

$xy_{′2}+xyy_{′}=yy_{′}$.