The differential equation y dy dx + x = a(a is any constant) repr… - Vidyadip

MCQ

The differential equation $y\frac{{dy}}{{dx}} + x = a$($a$ is any constant) represents

A
A set of circles having centre on the $y$-axis
✓
A set of circles centre on the $x$-axis
C
A set of ellipses
D
None of these

✓

Answer

Correct option: B.

A set of circles centre on the $x$-axis

b
(b) We have $y\frac{{dy}}{{dx}} + x = a$or$ydy + xdx = adx$

Integrating, we get $\frac{{{y^2}}}{2} + \frac{{{x^2}}}{2} = ax + c$

or ${x^2} + {y^2} - 2ax + k = 0$,

which represents a set of circles having centre on $x$-axis.

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

What is the degree of the differential equation:
$\text{y}=\text{x}\frac{\text{dy}}{\text{dx}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{-2}?$

If ${\sin ^{ - 1}}\left( {\frac{{2a}}{{1 + {a^2}}}} \right) + {\sin ^{ - 1}}\left( {\frac{{2b}}{{1 + {b^2}}}} \right) = 2{\tan ^{ - 1}}x,$ then $x = $

The projection of the line segment joining the points $(1,-1,3)$ and $(2,-4,11)$ on the line joining the points $(-1,2,3)$ and $(3,-2,10)$ is

Let $\text{f(x)}=\frac{\tan\Big(\frac{\pi}{4}-\text{x}\Big)}{\cot2\text{x}},\text{ x}\neq\frac{\pi}{4}$ The value which should be assigned to $f(x)$ at $\text{x}=\frac{\pi}{4},$ so that it is continuous everywhere is:

$\int_1^2 {\frac{{\cos (\log x)}}{x}} \,dx = $

$\int \frac{1}{x \sqrt{x^4-1}} d x=?$

The value of f(0), so that the function $\text{f(x)}=\frac{2-(256-7\text{x})^{\frac{1}{8}}}{(5\text{x}+32)^\frac{1}{5}-2},\text{ x}\neq0$ is continuous everywhere, is given by:

If $a = 2i + 5j$ and $b = 2i - j,$ then the unit vector along $a+b$ will be

Two matrix $P =\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $Q ^{ T }=\left[\begin{array}{rrr}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right]$, Find $P-Q$ :

$\int\limits_{\frac{\pi }{6}}^{\frac{{5\pi }}{6}} {\left( {\frac{1}{2}{{(3\sin \theta )}^2} - \frac{1}{2}{{(1 + \sin \theta )}^2}} \right)\,d\theta } $