If y = c e^ ^ - 1 x , then corresponding to this the differential… - Vidyadip

MCQ

If $y = c{e^{{{\sin }^{ - 1}}x}}$, then corresponding to this the differential equation is

✓
$\frac{{dy}}{{dx}} = \frac{y}{{\sqrt {1 - {x^2}} }}$
B
$\frac{{dy}}{{dx}} = \frac{1}{{\sqrt {1 - {x^2}} }}$
C
$\frac{{dy}}{{dx}} = \frac{x}{{\sqrt {1 - {x^2}} }}$
D
None of these

✓

Answer

Correct option: A.

$\frac{{dy}}{{dx}} = \frac{y}{{\sqrt {1 - {x^2}} }}$

a
(a) $y = c{e^{{{\sin }^{ - 1}}x}}$. Differentiate it w.r.t. $x$, we get

$\frac{{dy}}{{dx}} = c{e^{{{\sin }^{ - 1}}x}}.\frac{1}{{\sqrt {1 - {x^2}} }} = \frac{y}{{\sqrt {1 - {x^2}} }}$ or $\frac{{dy}}{{dx}} = \frac{y}{{\sqrt {1 - {x^2}} }}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The equation of the circumcircle of the triangle formed by the lines $y + \sqrt 3 x = 6,\;y - \sqrt 3 x = 6,$ and $y = 0$, is

The sum $\frac{3}{{{1^2}}} + \frac{5}{{{1^2} + {2^2}}} + \frac{7}{{{1^2} + {2^2} + {3^2}}} + ....$ upto $11-$ terms is

${\left( {\frac{{\cos \theta + i\sin \theta }}{{\sin \theta + i\cos \theta }}} \right)^4}$equals

If vertices of any quadrilateral are $(0, -1), \,(2,1),\, (0, 3)$ and $(-2,1)$, then it is a

$\int_{ - \pi }^\pi {{{(\cos px - \sin qx)}^2}dx} $ is equal to (where $p$ and $q$ are integers)

The length of the perpendicular drawn from the point $(5, 4, -1)$ on the line $\frac{{x - 1}}{2} = \frac{y}{9} = \frac{z}{5}$ is

Let $f (x)$ be integrable over $(a, b) , b > a > 0$.

If $I_1 = \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{3}} \, f (\tan\, \theta + \cot\, \theta )\cdot sec^2\, \theta\, d\, \theta$ &

$I_2 = \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{3}} \, f (\tan\, \theta + \cot\, \theta )\cdot cosec^2\, \theta\, d \, \theta$ ,

then the ratio $\frac{{{I_1}}}{{{I_2}}}$ :

Let $f(x)=2^x-x^2, x \in R$. If $m$ and $n$ are respectively the number of points at which the curves $y=f(x)$ and $y=f^{\prime}(x)$ intersects the $x$-axis, then the value of $m+n$ is

For $p\,>\,0$, a vector $\vec{v}_{2}=2 \hat{i}+(p+1) \hat{j}$ is obtained by rotating the vector $\vec{v}_{1}=\sqrt{3} p \hat{i}+\hat{j}$ by an angle $\theta$ about origin in counter clockwise direction. If $\tan \theta=\frac{(\alpha \sqrt{3}-2)}{4 \sqrt{3}+3}$, then the value of $\alpha$ is equal to $....$

$\mathop {\lim }\limits_{x \to 0} \frac{{{y^2}}}{x} = ........$, where ${y^2} = ax + b{x^2} + c{x^3}$