The solution of the differential equation dy dx = x( x + x)is - Vidyadip

MCQ

The solution of the differential equation $\frac{{dy}}{{dx}} = \sec x(\sec x + \tan x)$is

✓
$y = \sec x + \tan x + c$
B
$y = \sec x + \cot x + c$
C
$y = \sec x - \tan x + c$
D
None of these

✓

Answer

Correct option: A.

$y = \sec x + \tan x + c$

a
(a) $\frac{{dy}}{{dx}} = \sec x(\sec x + \tan x)$ ==> $\frac{{dy}}{{dx}} = {\sec ^2}x + \sec x\tan x$

Now integrating both sides, we get $y = \tan x + \sec x + c$.

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 STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The area of region $\{ \,(x,\,y):{x^2} + {y^2} \le 1 \le x + y\} $ is

The value of the function $f (x) = 1 + x + \int\limits_1^x {} \, (ln^2t + 2\, lnt)\, dt$ where $f ‘ (x)$ vanishes is :

If the minimum value of an objective function $Z=a x+b y$ occurs at two points $(3,4)$ and $(4,3)$ then

$\left| {\,\begin{array}{*{20}{c}}{b + c}& a& a\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right| = $

The function $y =\frac{{2x\,\, - \,\,1}}{{x\,\, - \,\,2}} (x \ne 2)$

Let $f (x) =$ $\frac{{{\text{g}}\,(x)}}{{{\text{h}}\,(x)}}$, where $g $ and $h$ are cotinuous functions on the open interval $(a, b)$. Which of the following statements is true for $a < x < b$ ?

The function $f(x)=2 x^3-15 x^2+36 x+4$ is maximum at $x=$

Let$\begin{vmatrix}\text{x}&2&\text{x}\\\text{x}^2&\text{x}&6\\\text{x}&\text{x}&6\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}.$ Then, the value of $5a + 4b + 3c + 2d + e$ is equal to:

Can $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$ be the direction cosines of any directed line?

A unit vector in the $xy - $ plane which is perpendicular to $4i - 3j + k$ is