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.