The general solution of the differential equation $\frac{dy}{dx} + \frac{y}{x} = x^2 + 5$ is ....

  • A
    $xy = \frac{x^4}{4} + \frac{5x^2}{2} + c$
  • B
    $xy = \frac{x^4}{4} - \frac{5x^2}{2} + c$
  • C
    $y = \frac{x^4}{4} + \frac{5x^2}{2} + c$
  • D
    $y = \frac{x^4}{4} - \frac{5x^2}{2} + c$

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If $y'' - 3y' + 2y = 0$ where $y(0) = 1$ and $y'(0) = 0$, then the value of $y$ at $x = \log_{e} 2$ is

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