Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
Choose the correct answer from the given four option.
The solution of the differential equation $\cos\text{x}\ \sin\text{y}\ \text{dx}+\sin\text{x}\ \cos\text{y}\ \text{dy}=0$ is:
  1. $\frac{\sin\text{x}}{\sin\text{y}}=\text{C}$
  2. $\sin\text{x}\ \sin\text{y}=\text{C}$
  3. $\sin\text{x}+\sin\text{y}=\text{C}$
  4. $\cos\text{x}\ \cos\text{y}=\text{C}$
✓

Answer

  1. $\sin\text{x}\ \sin\text{y}=\text{C}$

Solution:

Given differential equation is

$\cos\text{x}\ \sin\text{y}\ \text{dx}+\sin\text{x}\ \cos\text{y}\ \text{dy}=0$

$\Rightarrow\cos\text{x}\ \sin\text{y}\ \text{dx}=-\sin\text{x}\ \cos\text{y}\ \text{dy}=0$

$\Rightarrow\frac{\cos\text{x}}{\sin\text{x}}\text{dx}=-\frac{\cos\text{y}}{\sin\text{y}}\text{dy}$

$\Rightarrow\cot\text{x}\ {\text{dx}}=-\cot\text{y}\ {\text{dy}}$

On integrating both sides, we get

$\log\ \sin\text{x}=-\log\ \sin\text{y}+\log\ \text{C}$

$\Rightarrow\log\ \sin\text{x}\ \sin\text{y}=\log\ \text{C}$

Carrying the exponent on both sides, we get

$\Rightarrow\sin\text{x}\ \sin\text{y}=\text{C}$

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

$i\times (j\times k)+j\times (k\times i)\,+k\times (i\times i)$ equals
→
Let function $F$ be defined as $f\left( x \right) = \int\limits_1^x {\frac{{{e^t}}}{t}dt\,,\,x > 0} $ then the value of the integral $\int\limits_1^x {\frac{{{e^t}}}{{t + a}}dt\,} $ , where $a > 0$ , is
→
$\int {{{\cos }^{ - 3/7}}} x{\sin ^{ - 11/7}}x\,\,dx = $
→
If $A=$ $\left[ {\begin{array}{*{20}{c}}{5a}&{ - b}\\3&2\end{array}} \right]$ and $A\;adj\;A = A\;{A^T},$ then $5a+b $ to :
→
If $\cos^{-1}\text{x}>\sin^{-1}\text{x},$ then:
  1. $\frac{1}{\sqrt2}<\text{x}\leq1$
  2. $0\leq\text{x}\leq\frac{1}{\sqrt2}$
  3. $-1\leq\text{x}<\frac{1}{\sqrt2}$
  4. $\text{x}>0$
→
The maximum number of equivalence relations on the set $A=\{1,2,3\}$ are
→
Let $a$ and $\mathrm{b}$ respectively be the points of local maximum and local minimum of the function $f(x)=2 x^{3}-3 x^{2}-12 x .$ If $A$ is the total area of the region bounded by $\mathrm{y}=\mathrm{f}(\mathrm{x})$, the $\mathrm{x}$-axis and the lines $x=a$ and $x=b$, then $4 A$ is equal to ..... .
→
For the system of linear equations :

$x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R$

consider the following statements :

$(A)$ The system has unique solution if $k \neq 2$, $k \neq-2$

$(B)$ The system has unique solution if $k =-2$.

$(C)$ The system has unique solution if $k =2$.

$(D)$ The system has no-solution if $k =2$.

$(E)$ The system has infinite number of solutions if $k \neq-2$

Which of the following statements are correct?

→
If $\text{y}=\frac{\text{ax}+\text{b}}{\text{x}^2+\text{c}},$ then $(2\text{xy}_1+\text{y})\text{y}_3=$
  1. 3(xy2 + y1) y2
  2. 3(xy1 + y2) y2
  3. 3(xy1 + y2) y1
  4. None of these
→
If $f(x) = 4x^3 -x^2 - 2x + 1$ and $g(x) = [ \begin{array}{*{20}{c}}{Min\,\,\,\left\{ {f(t)\,\,\,\,0\,\, \le \,\,t\,\, \le \,\,x} \right\}}&{;\,\,\,\,0\,\, \le \,\,x\,\, \le \,\,1}\\{3\,\, - \,\,x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}&{;\,\,\,\,1\,\, < \,\,x\,\, \le \,\,2}\end{array}$ then $g\left( {\frac{1}{4}} \right) + g\left( {\frac{3}{4}} \right) + g\left( {\frac{5}{4}} \right)$ has the value equal to
→