- #1

- 708

- 20

[tex]\frac{dy}{dx}=\int^x_0 \varphi(t)dt[/tex]

we can write

[tex]dy=dx\int^x_0 \varphi(t)dt[/tex]

Now I can integrate it

[tex]\int^{y(x)}_{y(0)}dt=\int^x_0dx'\int^x_0\varphi(t)dt[/tex]

Is this correct?

Or I should write it as

[tex]\int^{y(x)}_{y(0)}dt=\int^x_0dx'\int^{x'}_0\varphi(t)dt[/tex]

Best wishes in new year and thank you for the answer.