Let $x_1 = y$ and $x_2 = y'$ and convert the ODE $$y'' + p(t)y'+ q(t)y = 0$$ to a system of two first-order ODEs in $x_1$ and $x_2$. Then show that if $x_1$ and $x_2$ form a fundamental set of solutions of your system, and if $y_1$ and $y_2$ form a fundamental set of solutions to the original ODE, then, up to a constant, the Wronskians are equal.
That is, $$W(x_1, x_2) = c~W(y_1, y_2)$$ for some non-zero constant $c ∈ R$