Is this DE linear?

1. Mar 2, 2013

cocopops12

(y^2)'' + (y^2)' + y^2 = 0

1) Is this DE linear?

What if we substitute y^2 = h
and solve for h
y = sqrt(h)

2) Would that be valid?
3) Would that be considered a somewhat trivial type of linearization?

2. Mar 2, 2013

rbj

if you make that substitution, it's linear.

3. Mar 3, 2013

Ratch

cocopuff,

No, of course not. The dependent variable is "y" and y^2 is nonlinear.

Yes.

No, linear DE's are not classified as trivial linear or nontrivial linear DE's.

Ratch

4. Mar 3, 2013

pasmith

Yes.

If you want y to be real-valued, then you will need $h(t) \geq 0$ for all t. Unfortunately the general solution of that particular ODE is oscillatory with a decaying amplitude, so there will be intervals where $h(t) < 0$ unless $h(t) = 0$ for all t.