The solution of the equation dy dx = e^ x - y + x^2 e^ - y is - Vidyadip

MCQ

The solution of the equation $\frac{{dy}}{{dx}} = {e^{x - y}} + {x^2}{e^{ - y}}$ is

✓
${e^y} = {e^x} + \frac{{{x^3}}}{3} + c$
B
${e^y} = {e^x} + 2x + c$
C
${e^y} = {e^x} + {x^3} + c$
D
$y = {e^x} + c$

✓

Answer

Correct option: A.

${e^y} = {e^x} + \frac{{{x^3}}}{3} + c$

a
(a) $\frac{{dy}}{{dx}} = {e^{x - y}} + {x^2}{e^{ - y}} = {e^{ - y}}({e^x} + {x^2})$

==> ${e^y}dy = ({x^2} + {e^x})dx$

Now integrating both sides, we get ${e^y} = \frac{{{x^3}}}{3} + {e^x} + c$.

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