Question
Asked Oct 24, 2019
53 views

Differential Equestion

Determine the Wronskian for each set of functions.
fx) 0, g(x)x, h(x) = e^x
zero
f(x) e(2x), g(x)= e^x
-e(3x)
f(x) 1, g(x) 1/x
=
f<(x) cos(x), g(x) = sin(x)
-e^(3x)
fx) 2, g(x) (cos(x)^2, h(x) = (sin(x))^2
f(x) x-5, g(x)x+ 2, h(x) 4x-3
zero
help_outline

Image Transcriptionclose

Determine the Wronskian for each set of functions. fx) 0, g(x)x, h(x) = e^x zero f(x) e(2x), g(x)= e^x -e(3x) f(x) 1, g(x) 1/x = f<(x) cos(x), g(x) = sin(x) -e^(3x) fx) 2, g(x) (cos(x)^2, h(x) = (sin(x))^2 f(x) x-5, g(x)x+ 2, h(x) 4x-3 zero

fullscreen
check_circle

Expert Answer

Step 1

You have asked a question with multiple sub parts. I will address the first three of them. Please post the balance questions separately.

The Wronskian for a set of three functions is as as shown on the white board.

help_outline

Image Transcriptionclose

f (r) g(x) Wronskian f'(x) g'(x) h'(x) |f" (x) g"(x) h"(x) h(ax)

fullscreen
Step 2

First sub part: Please see the white board. Since all the elements in the first column of the determinant is zro, hence the entire determinant will turn out to be zero.

help_outline

Image Transcriptionclose

Wronskian o 1 e=0 0 0 e

fullscreen
Step 3

Second sub part:

Please see ...

help_outline

Image Transcriptionclose

|f (x) g(x) |f'(x) g' (x) Wronskian |2e2 , 2πT2e2πer

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative