can you help mw with this question

[queen yew]

separation of variables

,,x' = \frac{\dd x}{\dd t}

[heady frigate]

lower quality boy (𝔸dωn𝓲²s)

[fluid ingot]

I didn’t understand:(

[queen yew]

Have you ever heard of the method separation of variables?

[fluid ingot]

No

😬

[queen yew]

uff

[fluid ingot]

😦

[queen yew]

I will show

You basically separate the variables

one side x

one side t

and integrate both sides

[queen yew]

do you understand?

,,\frac{\dd x}{\dd t} = (x+1)(\log t)e^{t+1+x} = (x+1)(\log t)e^te^1e^x

[heady frigate]

lower quality boy (𝔸dωn𝓲²s)

[queen yew]

,,\iff \int \frac{1}{(x+1)e^x} : \dd x = \int e \log t \cdot e^t : \dd t

[heady frigate]

lower quality boy (𝔸dωn𝓲²s)

[queen yew]

Now this looks nasty

I give up

[fluid ingot]

Yes ahaha but i understand i think