The solution of the equation $(1 + x^2)\frac{dy}{dx} = 1$ is

  • A
    $y = \log(1 + x^2) + c$
  • B
    $y + \log(1 + x^2) + c = 0$
  • C
    $y - \log(1 + x) = c$
  • D
    $y = \tan^{-1}x + c$

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The general solution of the differential equation $\frac{dy}{dx} = e^{x+y} + x^2 e^{x^3+y}$ is (where $C$ is a constant of integration):

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