Question

Match the second order linear equations with the Wronskian of (one of) their fundamental solution sets.

y'' - (2/t)y' + 8y = 0
y'' - ln(t)...

Answer 1

To match the second order linear equations with their Wronskian, we need to compute the Wronskian for each equation's fundamental solution set.

Step-by-step explanation:

The Wronskian is a determinant used to determine the linear independence of solutions to a second-order linear differential equation. To match the Wronskian with the second order linear equations, we need to compute the Wronskian for each equation's fundamental solution set.

For the equation y'' - (2/t)y' + 8y = 0, the fundamental solution set is {t^4, t^(-4)}. The Wronskian of this solution set is W(t) = t^(-8) + 4t^(-6).

For the equation y'' - ln(t)y = 0, the fundamental solution set is {t, t ln(t)}. The Wronskian of this solution set is W(t) = -t^2 ln(t) - t.