Download App

9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The differential equation $2xy\,\, dy = (x^2 + y^2 + 1) dx$ determines
  • A
    A family of circles with centre on $x-$ axis
  • B
    A family of circles with centre on $y-$ axis
  • ✓
    A family of rectangular hyperbola with centre on $x-$ axis
  • D
    A family of rectangular hyperbola with centre on $y-$ axis
✓

Answer

Correct option: C.
A family of rectangular hyperbola with centre on $x-$ axis
c
$2 x y d y=\left(x^{2}+1\right) d x+y^{2} d x$

$\Rightarrow \frac{2 x y d y-y^{2} d x}{x^{2}}=\left(1+\frac{1}{x^{2}}\right) d x$

$\Rightarrow d\left(\frac{y^{2}}{x}\right)=d\left(x-\frac{1}{x}\right)$

$\Rightarrow \frac{y^{2}}{x}=x-\frac{1}{x}+c \Rightarrow y^{2}=x^{2}-1+c x$

$\Rightarrow\left(x+\frac{c}{2}\right)^{2}-y^{2}=1+\frac{c^{2}}{4}$

which represents a family of rectangular hyperbolas with centre on $\mathrm{x}$ -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 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

Area between the curves $y = x^3$ and $y = \sqrt x$ is
→
If three vectors $a = 12i + 4j + 3k , b = 8i - 12j - 9k$ and  $c = 33i - 4j - 24k$ represents $a$  cube, then its volume will be
→
$\int {\frac{{{x^2}}}{{\left( {{x^2} + 1} \right)\left( {{x^2} + 4} \right)}}\,} dx$ is equal to
→
If $(\vec{a}+3 \vec{b})$ is perpendicular to $(7 \vec{a}-5 \vec{b})$ and $(\vec{a}-4 \vec{b})$ is perpendicular to $(7 \vec{a}-2 \vec{b})$, then the angle between $\vec{a}$ and $\vec{b}$ (in degrees) is $......$
→
The vector $\left( {\hat i \times \vec a.\vec b} \right)\hat i + \left( {\hat j \times \vec a.\vec b} \right)\hat j + \left( {\hat k \times \vec a.\vec b} \right)\hat k$ is equal to
→
If $f(x)\, = \,2\,{\tan ^{ - 1}}\,x\, + \,{\sin ^{ - 1}}\,\left( {\frac{{2x}}{{1 + {x^2}}}} \right),x > 1\,$ then $f\,(5)$ is equal to
→
Let $\alpha \in(0, \infty)$ and $A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$. If $\operatorname{det}\left(\operatorname{adj}\left(2 \mathrm{~A}-\mathrm{A}^{\mathrm{T}}\right) \cdot \operatorname{adj}\left(\mathrm{A}-2 \mathrm{~A}^{\mathrm{T}}\right)\right)=2^8$, then $(\operatorname{det}(\mathrm{A}))^2$ is equal to :
→
The area of the curve $x{y^2} = {a^2}(a - x)$ bounded by $y -$ axis is
→
$\int {(\sqrt {\tan x}  + \sqrt {\cot x} )} $ is equal to-
→
If $\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^{2} \theta} d \theta=A \log _{e}|B(\theta)|+C$ where $C$ is a constant of integration, then $\frac{ B (\theta)}{ A }$ can be
→