Differential Equations

[Guest]

Solve the following diff equation

2y[(y^2)-x] dy=dx

[Guest]

Solve the following diff equation

2y[(y^2)-x] dy=dx

Solve the following diff equation

2y[(y^2)-x] dy=dx

[quote="Guest"]Solution:
[tex]y'=1/x'[/tex]
and consider x as the dependent variable; then
[tex]2y[y²─x]=x'[/tex]
[tex]x'+2yx = ─2y²[/tex]
It is a linear differential equation, easy to solve,
considering the change of variable x=uv.
Also it is possible considerar it as a Bernoulli equation.