Question

3
B are constants.
6. Find the differential equation of the family of curves Ax2 + By2 = 1, where A, B are arbitrary
constants.​

Answer 1

the differential equation of Ax²+By²=1

here 2 cases arise i.e -

case(1)

differentiate wrt x

=> d(Ax²+By²)/dx =d(1)/dx

=> 2Ax+2By*dy/dx =0

case(2)

differentiate wrt y

=>d(Ax²+By²)/dy=d(1)/dy

=>2Ax*dx/dy+2By=0

chose one of the case as respective with differential variable required