Show that the given functions are linearly independent on the interval I and find a second-order linear homogeneous equation having the pair as a fundamental set of solutions.

Y1(x) = x , y2(x) = x^2, I = (0, infinity)

Question

Show that the given functions are linearly independent on the interval I and find a second-order linear homogeneous equation having the pair as a fundamental set of solutions.

Y1(x) = x , y2(x) = x^2, I = (0, infinity)

anonymous · Answer

Are you familiar with the Wronskian? I'd use that to check for linear independence first.

anonymous · Answer

Okay, so using y1(x)y2'(x) - y2(x)y1'(x) 

I get W[y1, y2] (x) = x^2

so what does that tell me??

anonymous · Answer

@zepdrix

anonymous · Answer

When the Wronskian is not equal to 0, the solutions are linearly independent.

anonymous · Answer

so then my general solution is just 

y = C1x + C2x^2

anonymous · Answer

I am really not sure what to do with the interval either? Or if this equation is what they are even looking for??