Q43 of 50 Page 193

Integrating factor of is:

Given differential equation

Divide throughout by x

Compare with we get and Q = x³ – 3

The IF integrating factor is given by e^∫Pdx

⇒ e^∫Pdx = e^-logx

Hence IF integrating factor is

Solution of the differential equation t any sec²x dx + tanx sec² ydy = 0 is:

Family y = Ax + A³ of curves is represented by the differential equation of degree:

Solution of is given by

The number of solutions of when y(1) = 2 is: