The solution of y ,dx - xdy + 3 x^2 y^2 e^ x^3 dx = 0 is - Vidyadip

MCQ

The solution of $y\,dx - xdy + 3{x^2}{y^2}{e^{{x^3}}}dx = 0$ is

✓
$\frac{x}{y} + {e^{{x^3}}} = c$
B
$\frac{x}{y} - {e^{{x^3}}} = 0$
C
$\frac{{ - x}}{y} + {e^{{x^3}}} = 0$
D
None of these

✓

Answer

Correct option: A.

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

a
(a) $ydx - xdy + 3{x^2}{y^2}{e^{{x^3}}}dx = 0$

$\frac{{ydx - xdy}}{{{y^2}}} + 3{x^2}{e^{{x^3}}}dx = 0$ ==> $d\left( {\frac{x}{y}} \right) + d{e^{{x^3}}} = 0$

On integrating, we get $\frac{x}{y} + {e^{{x^3}}} = c$

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