The differential equation y , ,dx = x , ,dy has a solution of the… - Vidyadip

MCQ

The differential equation $\cot y\,\,dx = x\,\,dy$ has a solution of the form

A
$y = \cos x$
✓
$x = c\sec y$
C
$x = \sin y$
D
$y = \sin x$

✓

Answer

Correct option: B.

$x = c\sec y$

b
(b) $\cot y.dx = x.dy$ ==> $\frac{{dx}}{x} = \frac{{dy}}{{\cot y}}$ ==> $\frac{{dx}}{x} = \tan y.dy$

Integrating both sides,

$\log x = \log \sec y + \log c$ ==> $x = c\sec y$.

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

More "M.C.Q (1 Marks)" from 9. differential equations→9. differential equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A population $p(t) $ of $ 1000 $ bacteria introduced into nutrient medium grows according to the relation $p(t) = 1000 + {{1000t} \over {100 + {t^2}}}$. The maximum size of this bacterial population is

In the interval $[0, 1]$ , the function ${x^2} - x + 1$ is

If $x = a(t + \sin t)$ and $y = a(1 - \cos t)$, then ${{dy} \over {dx}}$ equals

The value of $(\hat{i} \times \hat{j}) \cdot \hat{j}+(\hat{j} \times \hat{i}) \cdot \hat{k}$ is:

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

Function f(x) = a^x is increasing on R, if:

a > 0
a < 0
0 < a < 1
a > 1

If $\text{A}=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ \text{a} & \text{b} & 2 \end{bmatrix},$ then aI + bA + 2 A² equals:

A
-A
ab A
None of these.

If $f(x)$ is twice differentiable polynomial function such that $f(1) = 1,f(2) = 4,f(3) = 9$, then

If the area bounded by $y = a{x^2}$ and $x = a{y^2}$, $a > 0$, is $1$, then $a = $

If A and B are square matrices of the same order, then (A + B)(A - B) is equal to:

A² - B²
A² - BA - AB - B²
A² - B² + BA - AB
A² - BA + B²+ AB