# Thread:

1. ## Second order non homogeneous differential equation

I have to solve this DE
((x+2)^2)y'' -2y=4

the hint says to get rid of the x+2 but I have no idea where to start from... do I have to replace x+2 with another variable or what?

2. I would replace the $x+2$ with $t=x+2,$ and you get

$\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=\dfrac {dy}{dx}.$ Hence, the DE becomes

$t^{2}\,\dfrac{d^{2}y}{dt^{2}}-2y=4.$

This equation is a Cauchy-Euler equation.
{"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": 4, "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": 0.9197782874107361, "perplexity_flag": "middle"}