The solution of the given differential equation dy dx + 2xy = y i… - Vidyadip

MCQ

The solution of the given differential equation $\frac{{dy}}{{dx}} + 2xy = y$ is

✓
$y = c{e^{x - {x^2}}}$
B
$y = c{e^{{x^2} - x}}$
C
$y = c{e^x}$
D
$y = c{e^{ - {x^2}}}$

✓

Answer

Correct option: A.

$y = c{e^{x - {x^2}}}$

a
(a) $\frac{{dy}}{{dx}} + (2x - 1)y = 0$; $I.F.$ $ = {e^{\int_{}^{} {(2x - 1)dx} }} = {e^{{x^2} - x}}$

Required solution is $y{e^{{x^2} - x}} = c$or$y = c{e^{x - {x^2}}}$.

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

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

The projection of the join of the two points (1, 4, 5), (6, 7, 2) on the line whose d.ss are (4, 5, 6) is:

The position vector of a point $C $ with respect to $ B $ is $i + j$ and that of $ B$ with respect to $A$ is $i - j.$ The position vector of $ C $ with respect to $A$ is

If $u = x{y^2}{\tan ^{ - 1}}\left( {{y \over x}} \right)$, then $x{u_x} + y{u_y} = $

If $x = {\sin ^{ - 1}}(3t - 4{t^3})$ and $y = {\cos ^{ - 1}}\,\,\sqrt {(1 - {t^2})} $, then ${{dy} \over {dx}}$ is equal to

Let $f:(0, \infty) \rightarrow R$ be given by $f(x)=\int_{\frac{1}{x}}^x e^{-\left(t+\frac{1}{t}\right)} \frac{d t}{t}$. Then

$(A)$ $f(x)$ is monotonically increasing on $[1, \infty)$

$(B)$ $f(x)$ is monotonically decreasing on $(0,1)$

$(C)$ $f(x)+f\left(\frac{1}{x}\right)=0$, for all $x \in(0, \infty)$

$(D)$ $f\left(2^x\right)$ is an odd function of $x$ on $R$

The general solution of the differential equation $(x + y)dx + xdy = 0$ is

Two dice are thrown. If it is known that the sun of the numbers on the dice was less than 6, than the probability of gettinga sum 3, is

$\int1.\text{dx}=$

$\text{x}+\text{k}$
$1+\text{k}$
$\frac{\text{x}^2}{2}+\text{k}$
$\log\text{x}+\text{k}$

For vectors $\vec{a}, \vec{b}, \vec{c}$, if $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$ and $|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=5$ then $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}=$ _________ .

The distance of the point having position vector $ - \,\hat i\, + \,2\hat j\, + 6\hat k$ from the straight line passing through the point $(2, 3, -4)$ and parallel to the vector $6\,\hat i\, + 3\hat j\, - 4\hat k$ is