The discussion centers on solving the differential equation x*y²(dy/dx) = y³ - x³. The proposed solution is (x³/3) + c = y/x. To verify the solution, participants recommend solving for y, taking the derivative, and substituting back into the original equation to check for equality. This method ensures the correctness of the solution and confirms its validity against the given differential equation.
PREREQUISITESStudents studying calculus, particularly those focusing on differential equations, as well as educators looking for methods to teach solution verification techniques.
Solve your result for y. Then, take the derivative & plug it into the given equation. See if you get equality.shemer77 said:Homework Statement
x*y2(dy/dx)=y3-x3
solve the problem
Homework Equations
The Attempt at a Solution
My answer was (x3/3)+c=y/x
there is no answer in the back of the book for this one so i just want to make sure i got it right