Solution Verification for Dy = 2y/x using y = Cx^2

[Dr Game]

Homework Statement

Verify that the function is a solution of the DE

$$Dy = \frac{2y}{x} , y = Cx^2$$

2. The attempt at a solution

$$LHS = Dy = D(Cx^2) = 2 Cx$$
$$RHS = \frac{2y}{x}$$

then... I really don't know what to do from there... do I just simply things?

 

[HallsofIvy]

Homework Statement

Verify that the function is a solution of the DE

$$Dy = \frac{2y}{x} , y = Cx^2$$

2. The attempt at a solution

$$LHS = Dy = D(Cx^2) = 2 Cx$$
$$RHS = \frac{2y}{x}$$

then... I really don't know what to do from there... do I just simply things?

Well, how about replacing that y in RHS with Cx²?

 

[Dr Game]

$$2Cx = \frac {2Cx^2}{x}$$

$$2Cx = 2Cx$$

is that possible?

 

[SunGod87]

$$2Cx = \frac {2Cx^2}{x}$$

$$2Cx = 2Cx$$

is that possible?

Yes, that's fine.