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

MCQ

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

A
$y = \log \cos x + cx$
B
$y = \log \sec x + {c_1}x + {c_2}$
C
$y = \log \sec x - {c_1}x + {c_2}$
✓
Both $(b)$ and $(c)$

✓

Answer

Correct option: D.

Both $(b)$ and $(c)$

d
(d) ${\cos ^2}x\frac{{{d^2}y}}{{d{x^2}}} = 1$ ==> $\frac{{{d^2}y}}{{d{x^2}}} = {\sec ^2}x$

On integrating, we get $\frac{{dy}}{{dx}} = \tan x \pm {c_1}$

Again integrating, we get $y = \log \sec x \pm {c_1}x \pm {c_2}$.

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