Download App

Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
Choose the correct answer from the given four option.
The solution of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}=\frac{1+\text{y}^2}{1+\text{x}^2}$ is:
  • A
    $\text{y}=\tan^{-1}\text{x}$
  • ✓
    $\text{y}-\text{x}=\text{k}(1+\text{xy})$
  • C
    $\text{x}=\tan^{-1}\text{y}$
  • D
    $\tan(\text{xy})=\text{k}$
✓

Answer

Correct option: B.
$\text{y}-\text{x}=\text{k}(1+\text{xy})$

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 common region determined by all the constraints of a linear programming problem is called:
→
If $\vec a = \vec i + 2\vec j + 3\vec k$ , $\vec b = 2\vec i + 3\vec j + \vec k$ , $\vec c = 3\vec i + \vec j + 2\vec k$ and $\alpha \vec a + \beta \vec b + \gamma \vec c =  - 3\left( {\hat i - \hat k} \right)$ . Then the triplet $\left( {\alpha ,\beta ,\gamma } \right)$ is
→
Let mininmm $m$ , $(m\in Z^+)$ is define as power of a square matrix $'A'$ such that $A^m = I$ . If $A^5 = I$ and $ABA^{-1} = B^2$ . then power of matrix $B$ is between
→
Let $f:(0,2) \rightarrow R$ be defined as $f( x )=\log _{2}\left(1+\tan \left(\frac{\pi x }{4}\right)\right)$ Then, $\lim _{n \rightarrow \infty} \frac{2}{n}\left(f\left(\frac{1}{n}\right)+f\left(\frac{2}{n}\right)+\ldots+f(1)\right)$ is equal to
→
If $y = {x^{{x^{x......\infty }}}}$, then ${{dy} \over {dx}} = $
→
$\int\limits_{ - \,a}^a {\,f\,(x)\,dx} $=
→
A function $f$ is defined as follows,

$f(x) =$ $\left\{ {\begin{array}{*{20}{c}}  {\sin \,x}&{if\,\,\,x\,\, \leqslant \,\,c} \\   {ax\, + \,b}&{if\,\,\,x\,\, > \,\,c} \end{array}} \right.$ where $c$ is a known quantity.

If $f$ is derivable at $x = c$ , then the values of $'a'$ $and$ $'b’$ are _____ $and$______ respectively

→
Let $f(x) = {\cos ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right) + {\sin ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right)$ then the value of $f(1) + f(2)$, is -
→
If a matrix has mm rows and nn columns then its order is:
→
Let $y=t^{10}+1$ and $x=t^8+1$, then $\frac{d^2 y}{d x^2}$ is equal to
→