Toronto Math Forum

MAT244--2019F => MAT244--Test & Quizzes => Quiz-2 => Topic started by: shizhiwei on October 04, 2019, 03:27:42 PM

Title: tut0702 quiz2
Post by: shizhiwei on October 04, 2019, 03:27:42 PM

determine whether the equation is exact or not
                               ((e^2)sin(y)−2ysin(x))−(3x−(e^x)sin(y))y′=0

                   let             M(x,y)=(e^x)sin(y)−2ysin(x)
                                    N(x,y)=−3x+(e^x)sin(y)


    simplify and we get    My(x,y)=(e^x)cos(y)−2sin(x)
                                    Nx(x,y)=−3+(e^x)sin(y)


   we can conclude that  My is not equal to Nx, therefore the diffrentiation equation is not exact