Question

Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone (3x+3x - 3y)dx + (xy? - x-2)dy = 0 Select all that apply. A. has an integrating factor p(x) or p(y) not equal to a constant OB. linear OC. separable D. exact E. none of the above

Answer 1

Identify the equation as separable, linear, exact, on howing an integrating factor that is a function of either xor y alone - (3x + 3 x 3y) dx + (xy - x ²) dy o n Solution: • Given differential equation is, C (3x + 3x ) dx + ( xy - x2) dy o This equation cannot be simplified as o cal motto f(x) dx = q (ydy where of (2) is function corrido 9(4) is function of So, given differential equation is not separable. o we see that the degree of the differential equation is 6. So, the differential equation is not linear • Given differential equation can be written as Mdx +Ndy so ..... (ii) Here, M = 3x + 3x²y Na ry - x2 Now, 32 and on = y + 2 * 3 since am I then the differential equation is not exact.

Now, on our comme say? 2xD now, amay - anyar -x (xs you) So, the given differential equation has an integrating factor in that is a function of x. The refore, the giren equation has an factor u(x) not equal to a constant integrating to