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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
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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