In a differential equation problem, y'=(y/t)^(1/2).
The answer provided by my professor is y=(t^(1/2) + C)^2. My question is...Can -((-t)^(1/2) +C)^2 also work? It seems to fit if you plug it back into the original equation, but I am wondering if there is a problem with using imaginary numbers when solving diffEQs. If so, why could we not use them?

Question

In a differential equation problem, y'=(y/t)^(1/2).
The answer provided by my professor is y=(t^(1/2) + C)^2. My question is...Can -((-t)^(1/2) +C)^2 also work? It seems to fit if you plug it back into the original equation, but I am wondering if there is a problem with using imaginary numbers when solving diffEQs. If so, why could we not use them?

anonymous · Answer

If you use $-t$ under the radical, your $t$ would have to be a negative number to avoid the complex/imaginary issue you brought up. This would completely change the initial conditions of $t$, had you been given an initial value problem. I'm by no means an expert on differential equations, so this is just the impression I get.

abb0t · Answer

I'm having trouble seeing the equation. But it looks like you have a first order linear differential equation...