The solution of the differential equation d^2 y d x^2 = - 1 x^2 i… - Vidyadip

MCQ

The solution of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} = - \frac{1}{{{x^2}}}$ is

✓
$y = \log x + {c_1}x + {c_2}$
B
$y = - \log x + {c_1}x + {c_2}$
C
$y = - \frac{1}{x} + {c_1}x + {c_2}$
D
None of these

✓

Answer

Correct option: A.

$y = \log x + {c_1}x + {c_2}$

a
(a) $\frac{{{d^2}y}}{{d{x^2}}} = - \frac{1}{{{x^2}}}$. Now integrating both sides, we get

$\frac{{dy}}{{dx}} = \frac{1}{x} + {c_1}$ ==> $y = \log x + {c_1}x + {c_2}$.

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