Question

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

Answer 1

Thank you for asking this question. Here is your answer:

x²/b²+y²a² = 1--------(1)

2x/b²+2yy′/b² = 0--------(2)

1/b²+(1a²) [yy′′+(y′)²]=0

1/b²=−[1a²](yy′′+(y′)²

−[x/a²][yy′′+(y′)²]+yy′/a² = 0

xyy′′+x(y′)²−yy′ = 0

If there is any confusion please leave a comment below.

Answer 2

Thank you for asking this question. Here is your answer:

x²/b²+y²a² = 1--------(1)

2x/b²+2yy′/b² = 0--------(2)

1/b²+(1a²) [yy′′+(y′)²]=0

1/b²=−[1a²](yy′′+(y′)²

−[x/a²][yy′′+(y′)²]+yy′/a² = 0

xyy′′+x(y′)²−yy′ = 0

If there is any confusion please leave a comment below.