Understanding and Solving DiffEq: x' = 2*x^(1/2)

[pergradus]

Homework Statement

I have the differential equation:

x' = 2*x^1/2

The Attempt at a Solution

I can see easily that the solution x = t² satisfies the equation, however wolfram tells me the solution is:

1/4 (4 t² + 4 t C + C²)

which also satisfies the solution... I'm wondering how do I solve this differential equation in order to get the solution Mathematic got?

 

[Mark44]

Homework Statement

I have the differential equation:

x' = 2*x^1/2

The Attempt at a Solution

I can see easily that the solution x = t² satisfies the equation, however wolfram tells me the solution is:

1/4 (4 t² + 4 t C + C²)

which also satisfies the solution... I'm wondering how do I solve this differential equation in order to get the solution Mathematic got?

This DE is separable. Write it as
dx/dt = 2x^1/2
=> dx/(2x^1/2) = dt

Now integrate both sides. Don't forget the constant of integration.