The solution of the differential equation dx + e^{(y - x)} dy = 0 is

Concept:

If the coefficient of dx is the only function of x and coefficient of dy is only a function of y in the given differential equation then we can separate both dx and dy terms and integrate both separately.

\(\smallint f\left( x \right)dx = \smallint g\left( y \right)dy\)

Calculation:

Given:

dx + e(y - x) dy = 0

We can solve the above differential equation as follows:

dx = - e(y - x) dy

dx = - e^y e^-x dy

\(e^x dx = - e^y dy\)

Integrating both sides we get,

ex = -ey + c

e^x + e^y = c