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

MCQ

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

✓
${e^{5x}} + {e^{5y}} = c$
B
${e^{5x}} - {e^{5y}} = c$
C
${e^{5x + 5y}} = c$
D
None of these

✓

Answer

Correct option: A.

${e^{5x}} + {e^{5y}} = c$

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

Multiply the equation by ${e^{3x + 3y}}$ ==> ${e^{5x}}dx + {e^{5y}}dy = 0$

On integrating, we get ${e^{5x}} + {e^{5y}} = 5c' = c$.

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