Solution of (1 + ex/y ) dx + ex/y (1 – x/y) dy = 0 is | MATH - VARIABLE SEPARABLE TYPE DIFFERENTIAL EQUATIONS | SolveeIt | Solveeit

Today, August 18

Question

Solution of (1 + e^x/y ) dx + e^x/y (1 – x/y) dy = 0 is

A

xe^x/y + x = c

B

ye^x/y – x = c

C

ye^x/y + y = c

D

ye^x/y + x = c

Answer

ye^x/y + x = c

Explanation

Solution

put $\frac{x}{y}$ = t Ž y = $\frac{1}{t}$ x or $\frac{dy}{dx} = \frac{1}{t}$ + x $\frac{dt}{dx}$