Download App

Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The general solution of the differential equation $x d y+y d x=0$ is:
  • ✓
    $x y=c$
  • B
    $x+y=c$
  • C
    $x^2+y^2=c^2$
  • D
    $\log y=\log x+c$
✓

Answer

Correct option: A.
$x y=c$
We have, $x d y+y d x=0$
$\Rightarrow x d y=-y d x $
$\Rightarrow \int \frac{d y}{y}=-\int \frac{d x}{x} $
$\Rightarrow \log y=-\log x+\log c $
$\Rightarrow y=\frac{c}{x}$
$\Rightarrow x y=\text { constant }$

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 Differential Equations→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 value of the determinant $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{c}\\\text{b}-\text{c}&\text{c}+\text{b}&\text{b}\\\text{c}+\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is:
→
If the vectors $2i - 3j + 4k,\,\,i + 2j - k$ and $xi - j + 2k$ are coplanar, then $x = $
→
A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is
→
Which of the following functions is differentiable at $x = 0$
→
The corner points of the bounded feasible region are $(0,1),(0,7),(2,7),(6,3)(6,0)(1,0)$ For the objective function $\mathrm{Z}=3 x-y$

$(i)$ At which point, $Z$ is minimum?

$(ii)$ At which point, $Z$ is maximum ?

$(iii)$ The maximum value of $\mathrm{Z}$ is $\ldots \ldots \ldots$

$(iv)$ The minimum value of $\mathrm{Z}$ is $\ldots \ldots \ldots$

→
If ${x^2} + {y^2} = t - \frac{1}{t},{x^4} + {y^4} = {t^2} + \frac{1}{{{t^2}}}$ then $\frac{{dy}}{{dx}}$ equals
→
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to.
→
If the vectors $3 \hat{i}+\lambda \hat{j}+\hat{k}$ and $2 \hat{i}-\hat{j}+8 \hat{k}$ are perpendicular, then $\lambda$ is equal to
→
If $f(x)=x^2 g(x)$ and $g(x)$ is twice differentiable, then $f^{\prime \prime}(x)$ is equal to
→
The number of points in $(-\infty,\infty)$ for which $\text{x}^{2}-\text{x}\sin\text{x}-\cos\text{x}=0,$ is:
→