# Question relating to solving equations with Green's functions

• Mar 9th 2012, 10:23 PM
rushton
Question relating to solving equations with Green's functions
An easy question hopefully. I have the solution to a differential equation

$y'+2ty=g(t)$

in the form

$y=\int^t_{t_{0}}g(\tau)G(t,\tau)d\tau$

where $G(t,\tau)$ is greens function thus

$y=\int^t_{t_{0}}g(\tau)e^{\tau^2-t^2}d\tau$

if I want to solve it for

$g(t) &=t, \ 1 \leq t \leq 2$

would I get

$y=\int^2_{1} \tau e^{\tau^2-4}d\tau$

I am just not sure about replacing the t in the equation with the upper limit.

Thanks guys/girls
{"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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8535842299461365, "perplexity": 1321.5573046089796}, "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": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281151.11/warc/CC-MAIN-20170116095121-00065-ip-10-171-10-70.ec2.internal.warc.gz"}