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 9. differential equations→9. 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

If $\sin y = x\cos (a + y),$ then ${{dy} \over {dx}} = $

A coin is tossed $3$ times. The probability of getting exactly two heads is

$\int_{\,2}^{\,3} {\frac{{dx}}{{{x^2} - x}} = } $

$f(x) = \left\{ \begin{array}{l}
2 - \left| {{x^2} + 5x + 6} \right|,\,\,\,x \ne - 2\\
{a^2} + 1,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = - 2
\end{array} \right.$ . Then the range of $a$ , so that $f(x)$ has maximum at $x = -2$, is

Let $f(x)=2^x-x^2, x \in R$. If $m$ and $n$ are respectively the number of points at which the curves $y=f(x)$ and $y=f^{\prime}(x)$ intersects the $x$-axis, then the value of $m+n$ is

Let f : R → R be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^\text{x}+\text{e}^{-\text{x}}}$ then f(x) is:

One-one onto.
One-one but not onto.
Onto but not one-one.
None of these.

If $\text{x}=\text{f}(\text{t})$ and $\text{y}=\text{g}(\text{t}),$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is equals to:

$\frac{\text{f}'\text{g}''-\text{g}'\text{f}''}{(\text{f}')^3}$
$\frac{\text{f}'\text{g}''-\text{g}'\text{f}''}{(\text{f}')^2}$
$\frac{\text{g}''}{\text{f}''}$
$\frac{\text{f}''\text{g}'-\text{g}''\text{f}'}{(\text{g}')^3}$

If $A =\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$, then $A ^{10}=$ __________ .

Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear.

If order of a matrix is 3 × 3, then it is a?

square matrix
rectangular matrix
unit matrix
None of these