# differential equation with substitution!!!

• February 4th 2009, 08:08 AM
crafty
differential 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????
• February 4th 2009, 08:23 AM
Henderson
First thing to notice is that if $u = y - x$, then $\frac{du}{dx} = \frac{dy}{dx} -1$.

Substituting into your equation, then, will give you:

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

Do you see where to take it from here?
• February 4th 2009, 01:40 PM
crafty
i got to the form int (1/(sin u + 1)) du = int dx but how do integrate the part on the left?
• February 4th 2009, 02:05 PM
Krizalid
Multiply top and bottom by $1-\sin u.$
• February 4th 2009, 03:52 PM
crafty
Quote:

Originally Posted by Henderson
First thing to notice is that if $u = y - x$, then $\frac{du}{dx} = \frac{dy}{dx} -1$.

Substituting into your equation, then, will give you:

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

Do you see where to take it from here?

i tried this but shouldn't the correct form be du/dx = sin (u) - 1 and not plus 1 like you wrote, Henderson??