The differential equation dy 3 4 xy = x* + y* is not separable as dx written. However, assuming x + 0, you can make the substitution v = (that is, y = vx ), dy in terms of dx and then write dv v, and x. (Remember y and v are dx functions of x, so use implicit differentiation.) This gives dy dx dv dx Using that result, you can rewrite the dy original equation æy° .4 = x* + y* as dx separable equation in v and x: +

Q: dy Find - by implicit differentiation. Jx + y +Vxy =4 dx

A: Given: x + y + xy = 4

Q: y=u (1+u³)* and u = (3x - 2)²

A:

Q: Find  dy/dx by implicit differentiation. x2/x+y = y2 + 4

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.