# Thread:

1. ## Determine whether the function is a solution of the DE?

Determine whether the function is a solution of the differential equation
y''' - 8y = 0

(a) y = cos(2x)
(b) y = e^(2x)

What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?

2. Find $y'''$ for each possibility and sub them back into the equation to check.

Sound good?

3. Well, you could differentiate the given functions and see if they satisfy the equation, i.e., you want to know if $y''' = 8y$.

4. $cos(2x)-8y=0$
I end up with
y = 1/8 cos(2 x) + C
What should i do with this solution?

Originally Posted by pickslides
Find $y'''$ for each possibility and sub them back into the equation to check.

Sound good?

5. Your derivative is not correct. $y'= -2\cdot \sin(2x)$.

6. So i am suppose to replace a&b with Y''' or with 8(y)
and what does the 3 ''' mean?

Originally Posted by lvleph
Your derivative is not correct. $y'= -2\cdot \sin(2x)$.

7. $y'''$ means the third derivative. You are suppose to use the solutions in a) and b) and plug them in the original DEQ. If $y$ from a) or b) satisfies $y''' + 8y =0$ then it is a solution to the DEQ.
From a)
$y''' = 8\cos(2x)$
and so
$8\cos(2x) - 8cos(2x) = 0$
So, a) is a solution to the DEQ. Now, check if b) works.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.902764081954956, "perplexity_flag": "middle"}