You can do the following. Once you get the output in Wolfram Alpha web page, say you have typed solve y'+x=0
, then in the output window, hover the mouse there, and select plain text
option

Then in the window which opens, select continue in computable notebook

Then a Wolfram Alpha notebook now opens showing the commands it used to generate the output on the web page. Like this

The commands are not evaluated. To evaluate them, hit the enter key in the first cell. This will now generate the output you saw at the Wolfram web page.
Then below the output cell, now type the command TeXForm[%]
to generate the Latex, like this

Then copy the Latex to clipboard and paste the latex to your Latex editor.