Question 4 x Your answer is incorrect. Try again. Solve the given differential equation. All solutions should be found. dy 3x2 6y ya 6r+ 3ry2 Do not enter an arbitary constant. ad Q ' = C, where C' is a constant of integration. 3 Question 4. Solution - Google Chrome edugen.wileyplus.com/edugen/shared/assignment/test/qsolution.uni?itemid= Solution Question 4 Let M = - (3 x2 - 6y - y3 ) and N = 6x + 3xy?. Rewrite the given equation as Mde + Ndy = 0. (1) Note that My = 6 + 3y? = NY . Hence (1) is exact. That means there is a function o (x, y) such that v, (x, y) = M and why (x, y) = N. Integrating the first of these equations with respect to I, we obtain (x,y) = bry + ry3 - 23 + h(y), where h (y) is an arbitrary function to be chosen so that the second equation Vy (x, y) = N must be satisfied. Thus, (Gry + ry3 - x3 + h (y)), =6x + 3xy? or h (y) = 0. We can choose h (y) = 0. Thus the solutions are given implicity by 6xy + xy3 - x3 = C, where O is any constant.Question 2 Solve the given differential equation. All solutions should be found. dy 31 5y y 514 3ry2 Do not enter an arbitary constant. Q C' = C, where O is a constant of integration