Differential equation

1. May 8, 2015

gonadas91

It is a general doubt about the following equation: Imagine I want to calculate an unknown function $$y(x)$$, and my starting equation is of the type

$$y(x)^{2}=\frac{1}{x^{2}Log^{2}(A(x)y(x)^{2})}$$

, then, am I allowed to start with the equation

$$y(x)=\frac{1}{xLog(A(x)y(x)^{2})}$$

and differenciate in both sides of the equation, to obtain a first order diferential equation to get y(x)?

(Note that the beginning equation is a trascendental equation, but why not trying to solve the first order ODE?)

Thank you

2. May 8, 2015

Brage

I dont see why this wouldn't be allowed but I'd assume setting $f(x)=y(x)^2$ and solving for $f(x)$ would be simpler. You can ofc use $log(a)^2=log(a)*log(a)=log(2a)$ to remove the square on the logarithmic function.

3. May 8, 2015

gonadas91

Mmm the last property of the logs is not valid. My question actually has to be with the modifications that are allowed on a differential equation. Also, the resulting differential equation using that is not depending on A(g) which annoys me somehow...

4. May 8, 2015

Brage

oh yeah ofc it isnt haha, too late for this here

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