using the substitution u = y-x solve dy/dx = sin(y-x) after substitution i get sin u but then how do integrate with respect to x????

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- Feb 4th 2009, 08:08 AMcraftydifferential equation with substitution!!!
using the substitution u = y-x solve dy/dx = sin(y-x) after substitution i get sin u but then how do integrate with respect to x????

- Feb 4th 2009, 08:23 AMHenderson
First thing to notice is that if $\displaystyle u = y - x$, then $\displaystyle \frac{du}{dx} = \frac{dy}{dx} -1$.

Substituting into your equation, then, will give you:

$\displaystyle \frac{du}{dx} = sin(u) +1$.

Do you see where to take it from here? - Feb 4th 2009, 01:40 PMcrafty
i got to the form int (1/(sin u + 1)) du = int dx but how do integrate the part on the left?

- Feb 4th 2009, 02:05 PMKrizalid
Multiply top and bottom by $\displaystyle 1-\sin u.$

- Feb 4th 2009, 03:52 PMcrafty