Wronskian-Differential Equations

Question

The equations below are matrices:

Consider the vectors $y^{(1)} (t)$=$\begin{pmatrix}t \\1 \end{pmatrix}$ and
$y^{(2)}$ (t)=$\begin{pmatrix}t^2 \\2t \end{pmatrix}$ (a) Compute the Wronskian of $y^{(1)}$ and $ y^{(2)}$. I have computed the wronskian and it came up to be $t^2$

(b)In what intervals are $y^{(1)}$ and $y^{(2)}$ linearly independent? Since the wronskian is not equal to 0, therefore it is linearly independent in any interval because any interval contains at least a non zero t-value

This is all I have done!!

And I am confused about the parts (c) and (d) The questions are;

(c ) What conclusions can be drawn about the coefficients in the system of homogeneous differential equations satisfied by $y^{(1)}$ and $y^{(2)}~$??

( d) Find the system of equations and verify the conclusion of part (c )

Can anybody help me???

Answer 1

Part b: $-\infty\ to +\infty$

part c: Not supposed be continuous at t= 0.

part d: you may want to use:

                                      2
            | 1  2t | = | a  b | | t t  |
            | 0  2  |   | c  d | | 1 2t |