 Hi and welcome to the session, let's work out the following question. The question says, form the differential equation of the following family of curves, that is x, y is equal to a into e raised to power x plus b into e raised to power minus x plus x squared. Let us see the solution to this question, here we are given x, y to be equal to a into e raised to power x plus b into e raised to power minus x plus x squared, we call this equation one, now differentiating both sides with respect to x we get x into dy by dx plus y, here we have applied the product rule is equal to a into e raised to power x because differentiation with respect to x of e raised to power x is e raised to power x minus b into e raised to power minus x plus 2x, we call this equation two, now again differentiating both the sides with respect to x we get x into d2y by dx2 plus 1 into dy by dx plus dy by dx is equal to a into e raised to power x plus b into e raised to power minus x plus 2, we call this equation three, now from equation one and equation three we get x into d2y by dx2 plus 2dy by dx is equal to xy minus x squared plus 2, so this is our answer to this question, I hope that you understood the solution and enjoyed the session, have a good day.