SOLUTION: The differential equation y−2y^3=(y^5+2x)y′ can be written in differential form: M(x,y)dx+N(x,y)dy=0 where M(x,y)=My answer is x/y^2, wrong ------N(x,y)= My answer is

Algebra ->  Expressions -> SOLUTION: The differential equation y−2y^3=(y^5+2x)y′ can be written in differential form: M(x,y)dx+N(x,y)dy=0 where M(x,y)=My answer is x/y^2, wrong ------N(x,y)= My answer is       Log On


   

Question 1184076: The differential equation
y−2y^3=(y^5+2x)y′
can be written in differential form:
M(x,y)dx+N(x,y)dy=0
where M(x,y)=My answer is x/y^2, wrong
------N(x,y)= My answer is y^3-((2x)/y^3), wrong
The term M(x,y)dx+N(x,y)dy becomes an exact differential if the left hand side above is divided by y^3. Integrating that new equation, the solution of the differential equation is
My answer (x/y^2)-(y^3/3)-2x=C , correct
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
M%28x%2Cy%29+=+y+-+2y%5E3 and N%28x%2Cy%29+=+-y%5E5+-+2x

After division by y%5E3,

∂(M%28x%2Cy%29%2Fy%5E3)/∂y =+-2%2Fy%5E3+= ∂(N%28x%2Cy%29%2Fy%5E3%29)/∂x,

and the new differential form becomes exact.