Is This ODE a Bernoulli Equation and Can It Be Solved with Substitution?

[Houeto]

consider ODE :

Show that the solution to this ODE is:

Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2?

Thanks

 

[Twigg]

It's separable. Divide both sides by $y^{2}$, multiply both sides by dx, and you'll see what I mean.

 

[Mark44]

Can someone tell what kind of ODE is it?

The DE is a first order, non-linear differential equation. It's first order, since the highest derivative is a first derivative. It's nonlinear, since the dependent variable is not first-degree.

As Twigg points out, it turns out to be separable, so you can manipulate it to get y and dy on one side and x and dx on the other. Solving DEs by separation is one of the first techniques presented in most diff. equation textbooks.

 

[Houeto]

Thanks Guys!