Question

Two solutions to $y'' - y = 0$ are $y_1 = e^t$, $y_2 = e^{-t}$. a) Find the Wronskian. $W =$ b) Are the functions $y_1 = e^t$, $y_2 = e^{-t}$ linearly independent or dependent? Independent Dependent Question 2 Calculate the Wronskian of $y_1 = 5x$ and $y_2 = 7x$. $W(x) =$ b) Are the functions $y_1 = 5x$, $y_2 = 7x$ linearly independent or dependent? Independent Dependent c) If the functions are linearly dependent, there exists coefficients $c_1$ and $c_2$ such that $c_1y_1 + c_2y_2 = 0$ Which of the following would satisfy this? $c_1 = 7$ and $c_2 = 5$ $c_1 = -7$ and $c_2 = 5$ $c_1 = 5$ and $c_2 = 7$ The functions are linearly independent.

          Two solutions to $y'' - y = 0$ are $y_1 = e^t$, $y_2 = e^{-t}$.
a) Find the Wronskian.
$W =$
b) Are the functions $y_1 = e^t$, $y_2 = e^{-t}$ linearly independent or dependent?
Independent
Dependent
Question 2
Calculate the Wronskian of $y_1 = 5x$ and $y_2 = 7x$.
$W(x) =$
b) Are the functions $y_1 = 5x$, $y_2 = 7x$ linearly independent or dependent?
Independent
Dependent
c) If the functions are linearly dependent, there exists coefficients $c_1$ and $c_2$ such that $c_1y_1 + c_2y_2 = 0$
Which of the following would satisfy this?
$c_1 = 7$ and $c_2 = 5$
$c_1 = -7$ and $c_2 = 5$
$c_1 = 5$ and $c_2 = 7$
The functions are linearly independent.

Two solutions to y” - y = 0 are y1 = e^t, y2 = e^-t.
a) Find the Wronskian.
W =
b) Are the functions y1 = e^t, y2 = e^-t linearly independent or dependent?
Independent
Dependent
Question 2
Calculate the Wronskian of y1 = 5x and y2 = 7x.
W(x) =
b) Are the functions y1 = 5x, y2 = 7x linearly independent or dependent?
Independent
Dependent
c) If the functions are linearly dependent, there exists coefficients c1 and c2 such that c1y1 + c2y2 = 0
Which of the following would satisfy this?
c1 = 7 and c2 = 5
c1 = -7 and c2 = 5
c1 = 5 and c2 = 7
The functions are linearly independent.

Added by Joshua J.

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