Question

Find the solution of $(1+e^{x/y})dx+e^{x/y}(1-x/y)dy=0$

• A. $x+y{e}^{\frac{x}{y}}=c$
• B. $x-y{e}^{\frac{x}{y}}=c$
• C. $x-y{e}^{\frac{y}{x}}=c$
• D. $x+y{e}^{\frac{y}{x}}=c$

Answer 1

The correct option is A $x+y{e}^{\frac{x}{y}}=c$

$(1+e^{x/y})dx+e^{x/y}(1-x/y)dy=0$
$dx+e^{x/y}(dx-\frac{x}{y}dy)+e^{x/y}dy=0$
or $dx+e^{x/y}\frac{ydx-xdy}{y}+e^{x/y}dy=0$
or $dx+y{e}^{x/y}d\left(\frac{x}{y}\right)+e^{x/y}dy=0$
or $dx+d\{y.e^{x/y}\}$ by product rule.
Integrating,we get,
$x+y{e}^{\frac{x}{y}}=c$