Okay, this is a three part question, and I need help with the second and third parts.

Part 1: Show that the implicit equation xy^2-y^3=c is a solution of the diff eq (3y-2x)y'=y. That's easy enough to do; I just find the first derivative of my original equation, plug it into the second and solve for y to verify that it is indeed a solution.

Part b: What is the value of the constant c if the solution must also satisfy the initial condition y(3)=2? My first thought here is to plug x=3 and y=2 into the first equation and solve for C, whch gives me C=4, but that doesn't seem right.

Question

Okay, this is a three part question, and I need help with the second and third parts.

Part 1: Show that the implicit equation xy^2-y^3=c is a solution of the diff eq (3y-2x)y'=y.  That's easy enough to do; I just find the first derivative of my original equation, plug it into the second and solve for y to verify that it is indeed a solution.  

Part b: What is the value of the constant c if the solution must also satisfy the initial condition y(3)=2?  My first thought here is to plug x=3 and y=2 into the first equation and solve for C, whch gives me C=4, but that doesn't seem right.

anonymous · Answer

Third part: what, if anything, does the existence and uniqueness theorem say about a solution at the point x=3, y=2?  Specifically, does a solution exist at this point?  I have no idea.