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99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations

The general solution of differential equation d y d x =e^ x+y +x^2 e^ x^3+y is (where C is a constant of integration.)

Options

  1. Ae ^ x + e ^ - y + 1 3 e ^ x ^3 = C
  2. Be^x-e^ -y - 1 3 e^ x^3 =C
  3. Ce^x-e^ -y + 1 3 e^ x^3 =C
  4. De^x-e^ -y + 1 3 e^ x^3 =C

Correct answer

A. e ^ x + e ^ - y + 1 3 e ^ x ^3 = C

Step-by-step solution

aligned & d y d x =e^ x+y +x^2 e^ x^3+y & d y d x =e^y (e^x+x^2 e^ x^3 ) & e^ -y d y= (e^x+x^2 e^ x^3 ) d x & -e^ -y +c=e^x+ 1 3 e^ x^3 & e^x+e^ -y + 1 3 e^ x^3 =c aligned

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