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.
Integrating factor of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}-\sec\text{x}=0$ is:
  1. $\cos\text{x}$
  2. $\sec\text{x}$
  3. $\text{e}^{\cos\text{x}}$
  4. $\text{e}^{\sec\text{x}}$
✓

Answer

  1. $\sec\text{x}$

Solution:

Given that, $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}-\sec\text{x}=0$

$\Rightarrow\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}=\sec\text{x}$

$\Big($It is a linear differential equation of form $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{P}\text{y}=\text{Q}\Big)$

Here, $\text{P}=\tan\text{x},\text{Q}=\sec\text{x}$

$=\text{I.F.}=\text{e}^{\int\text{Pdx}}$

$=\text{e}^{\int\tan\text{x}\text{dx}}$

$=\text{e}^{(\log\sec\text{x})}$

$=\sec\text{x}$

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

Let $A = \left( {\begin{array}{*{20}{c}}0&0&{ - 1}\\0&{ - 1}&0\\{ - 1}&0&0\end{array}} \right)$, the only correct statement about the matrix $A$ is
→
The eqution of the plane $\vec{\text{r}}=\hat{\text{i}}-\hat{\text{j}}+\lambda(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})+\mu(\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}})$ in scalar product from is:
→
The area bounded by $y = - {x^2} + 2x + 3$  and  $y = 0$ is
→
The inverse of $\left[ {\begin{array}{*{20}{c}}3&5&7\\2&{ - 3}&1\\1&1&2\end{array}} \right]$ is
→
Let $a_{n}=\int_{-1}^{n}\left(1+\frac{x}{2}+\frac{x^{2}}{2}+\frac{x^{3}}{3}+\ldots \ldots .+\frac{x^{n-1}}{n}\right) d x$ for $n \in N$. Then the sum of all the elements of the set $\left\{n \in N: a_{n} \in(2,30)\right\}$ is $...........$
→
$\left[ \begin{array}{l}\,\,\,1\\ - 1\\\,\,\,2\end{array} \right]\,\,[2{\rm{ }}\,\,1{\rm{ }} - 1]$ =
→
$AB,BC$ are diagonals of adjacent faces of a rectangular box with its centre at the origin, its edges parallel to the co-ordiantes axes.If the angles $BOC, COA$ and $AOB$ are $\alpha,\beta$ and $\gamma$ respectively, then $cos\,\,\alpha + cos\,\,\beta + cos\,\,\gamma$ is-
→
Mark the correct alternative in the following question for the binary operation * on Z defined by a * b = a + b + 1, the identity element is:
  1. 0
  2. -1
  3. 1
  4. 2
→
The ordered pair $(a, b)$, for which the system of linear equations  $3 x-2 y+z=b$  ;  $5 x-8 y+9 z=3$  ;  $2 x+y+a z=-1$ has no solution, is
→
Let $M$ be any $3 \times 3$ matrix with entries from the set $\{0,1,2\}$. The maximum number of such matrices, for which the sum of diagonal elements of $M ^{ T } M$ is seven, is .............
→