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Question 4. (15 pts) Let $y_1(x) = \sin x$ and $y_2(x) = x^2$. (a) Find the Wronskian $W[y_1, y_2]$. (b) Determine whether $y_1$ and $y_2$ are linearly dependent. Justify your answer. (c) Can $y_1$ and $y_2$ be solutions of the same differential equation in the form of $y'' + p(x)y' + q(x)y = 0$ (where $p(x)$ and $q(x)$ are continuous functions)? Why or why not?

          Question 4. (15 pts) Let $y_1(x) = \sin x$ and $y_2(x) = x^2$.
(a) Find the Wronskian $W[y_1, y_2]$.
(b) Determine whether $y_1$ and $y_2$ are linearly dependent. Justify your answer.
(c) Can $y_1$ and $y_2$ be solutions of the same differential equation in the form of
$y'' + p(x)y' + q(x)y = 0$ (where $p(x)$ and $q(x)$ are continuous functions)? Why
or why not?

Question 4. (15 pts) Let y1(x) = sin x and y2(x) = x^2.
(a) Find the Wronskian W[y1, y2].
(b) Determine whether y1 and y2 are linearly dependent. Justify your answer.
(c) Can y1 and y2 be solutions of the same differential equation in the form of
y” + p(x)y' + q(x)y = 0 (where p(x) and q(x) are continuous functions)? Why
or why not?

Added by Elizabeth P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/05/2023

Step 1

The Wronskian of two functions y1 and y2 is defined as the determinant of the matrix: W[y1, y2] = | y1 y2 | | y1' y2' | where y1' and y2' are the derivatives of y1 and y2 with respect to x. In this case, y1 = sin(x) and y2 = x^2. Taking the Show more…

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Question 4.15 pts Let y1 = sin(x) and y2 = x^2. a) Find the Wronskian W[y1, y2]. b) Determine whether y1 and y2 are linearly dependent. Justify your answer. c) Can y1 and y2 be solutions of the same differential equation in the form of y'' + p(x)y' + q(x)y = 0 (where p(x) and q(x) are continuous functions)? Why or why not?