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 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

If $f(x) = \left\{ \begin{array}{l}{\sin ^{ - 1}}|x|,{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,{\rm{when\,\, }}x = 0\end{array} \right.$ then

Let $\lambda \in R , \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$ If $((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}$, then $|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2$ is equal to

Let us consider a curve, $\mathrm{y}=\mathrm{f}(\mathrm{x})$ passing through the point $(-2,2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x)+x f^{\prime}(x)=x^{2}$ Then :

If A and B are two events such that $\text{P(A)}=\frac{1}{2},\text{P(B)}=\frac{1}{3},\text{P}(\text{A}|\text{B})=\frac{1}{4},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals.

The number of solutions for the equation $ 2\sin ^{ -1 }{ \sqrt { { \text{x} }^{ 2 }- \text{x}+1 } } +\cos ^{ -1 }{ \sqrt { { \text{x} }^{ 2 }- \text{x} } } =\frac { 3\pi }{ 2 }$ is:

1
2
3
Infinite

Let f : R → R be a function defined by f(x) = x³ + 4, then f is:

Injective.
Surjective.
Bijective.
None of these.

If $y = 1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + .....\infty ,$ then ${{dy} \over {dx}} = $

If $\mathrm{y}=\mathrm{y}(\mathrm{x})$ is an implicit function of $\mathrm{x}$ such that $\log _{e}(x+y)=4 x y$, then $\frac{d^{2} y}{d x^{2}}$ at $x=0$ is equal to .... .

Let $f(x) = e^x - e^{-x} + cosx$, then $f(x)$ is

If ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}1&0\\a&b\end{array}\,} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}1&0\\c&d\end{array}} \right|$, then ${\Delta _2}{\Delta _1}$is equal to