The solution of the differential equation x y dy dx = 1 is - Vidyadip

MCQ

The solution of the differential equation $x\sec y\frac{{dy}}{{dx}} = 1$ is

A
$x\sec y\tan y = c$
✓
$cx = \sec y + \tan y$
C
$cy = \sec x\tan x$
D
$cy = \sec x + \tan x$

✓

Answer

Correct option: B.

$cx = \sec y + \tan y$

b
(b) $x\sec y\frac{{dy}}{{dx}} = 1$ ==> $\sec ydy = \frac{{dx}}{x}$

On integrating both sides, we get

$\log (\sec y + \tan y) = \log x + \log c$ ==> $\sec y + \tan y = cx$.

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 STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\left[\begin{array}{ll}x+y & 2 x+z \\ x-y & 2 z+w\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ 0 & 10\end{array}\right]$, then the values of $x, y, z$ and $w$ respectively are

The value of $\int_{}^{} {\frac{{dx}}{{\sqrt x \,(x + 9)}}dx} $ is equal to

The differential equation which represents the family of curves $y = {c_1}{e^{{c_2}x}}$, where ${c_1}$ and $\;{c_2}$ are arbitrary constants is

Suppose $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ is a real matrix with non-zero entries, $\alpha d-b c=0$ and $A^2=A$. Then, $a + d$ equals

If $a = (1,\,\,1,\,\,1),\,\,c = (0,\,\,1,\,\, - 1)$ are two vectors and $b$ is a vector such that $a \times b = c$ and $a\,.\,b = 3,$ then $b$ is equal to

Area of the region bounded by the curve $\text{y}=\sqrt{49-\text{x}^2}$ and the x - axis is:

If for $x \in \left( {0,\frac{1}{4}} \right)$ , the derivative of ${\tan ^{ - 1}}\left( {\frac{{6x\sqrt x }}{{1 - 9{x^3}}}} \right)$ is $\sqrt x \cdot g\left( x \right)$ then $g\left( x \right)$ equals:

$\int\frac{10\text{x}^9+10^\text{x}\log_\text{e}10}{10^\text{x}+\text{x}^{10}}\text{dx}$ is equal to:

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

If $a = - 3i + 7j + 5k,$ $b = - 3i + 7j - 3k$, $c = 7i - 5j - 3k$ are the three coterminous edges of a parallelopiped, then its volume is