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NDA2010MathematicsDifferential EquationsActual

What is the solution of the differential equation 3 e^x tan y~ d x+ (1+e^x ) 2 y~ d y=0 ? where c is a constant of integration.

Options

  1. A(1+e^x ) y=c
  2. B(1+e^x )^3 y=c
  3. C(1+e^x )^2 y=c
  4. D(1+e^x ) ^2 y=c

Correct answer

B. (1+e^x )^3 y=c

Step-by-step solution

aligned & (1+e^x ) ^2 y d y=-3 e^x y d x & ^2 y y d y= -3 e^x 1+e^x d x aligned Using log on both side or y=-3 (1+e^x )+ c or y= c (1+e^x )^3 or y= c (1+e^x )^3 (1+e^x )^3 y=c

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