Question

Determine whether the equation is exact. If it is, then solve it (2xy + 3)dx + (x²-6) dy=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The equation is exact and an implicit solution in the form F(x,y)=Cis-C, where is an arbitrary constant (Type an expression using x and y as the variables.) OB. The equation is not exact,

Answer 1

Ans: A) The equation is exact and an implicit solution is of the form F(x,y)=C is    =C

z-y + 3.0 - 64

Explanation

Sol (2x4+3) dx + (x2-6d4 = 0 M dx + Ndy=0 am Sy + OM ду (2x4+3) = 2xto - 2x dy IN ax & fc (X²6) 2x-0 = 2x Clearly am dy - DN dx > Equation is exact.) Now, solution is Given by C M doc + SNE dy y as a constant integration only those constant terms or N which is free from a Hore N=x2-6 NE = -6 Hence, solution is given by S (2x4+3) dx - S6 dy = 0 24 x + 3x - 69 = 6 x²y +3X-64=c ( +

Answer 2

Determine whether the following equations is exact, if it is then solved it. (cos?cos?+2?)??− (sin?sin?+2?)??=0

Answer 3

Determine whether the following equations is exact, if it is then solved it. (cos?cos?+2?)??− (sin?sin?+2?)??=0