The solution of the equation d y d x = e^x+e^ -x e^x-e^ -x is : - Vidyadip

MCQ

The solution of the equation $\frac{d y}{d x}=\frac{e^x+e^{-x}}{e^x-e^{-x}}$ is :

A
$y=\log \left(e^x+e^{-x}\right)+c$
✓
$y=\log \left(e^x-e^{-x}\right)+c$
C
$y=\log \left(e^x+1\right)+c$
D
$y=\log \left(1-e^{-x}\right)+c$

✓

Answer

Correct option: B.

$y=\log \left(e^x-e^{-x}\right)+c$

(B)
$
\frac{d y}{d x}=\frac{e^x+e^{-x}}{e^x-e^{-x}}
$
Separating the variables
$
d y=\frac{e^x+e^{-x}}{e^x-e^{-x}} d x
$
Hence $\quad \int d y=\int \frac{e^x+e^{-x}}{e^x-e^{-x}} d x$ $
\Rightarrow \quad y=\log \left(e^x-e^{-x}\right)+c
$
Hence the correct choice is (B).

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 $\frac{d}{{dx}}F(x) = \left( {\frac{{{e^{\sin x}}}}{x}} \right)\,;\,x > 0$. If $\int_{\,1}^{\,4} {\frac{3}{x}{e^{\sin {x^3}}}dx = F(k) - F(1)} $, then one of the possible value of $k$, is

If $u = {({x^2} + {y^2} + {z^2})^{3/2}}$, then ${\left( {{{\partial u} \over {\partial x}}} \right)^2} + {\left( {{{\partial u} \over {\partial y}}} \right)^2} + {\left( {{{\partial u} \over {\partial z}}} \right)^2} = $

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

Let $f(x)=x^3+a x^2+b x+c$ where $a, b, c$ are real numbers. If $f(x)$ has a local minimum at $x=1$ and a local maximum at $x=-\frac{1}{3}$ and $f(2)=0$, then $\int_{-1}^1 f(x) d x$ equals

Evaluate $\begin{bmatrix}5&4&3\\3&4&1\\5&6&1\end{bmatrix}$is:

4
-24
-8
8

A farmer $F _1$ has a land in the shape of a triangle with vertices at $P (0,0), Q (1,1)$ and $R (2$, $0)$. From this land, a neighbouring farmer $F_2$ takes away the region which lies between the side $PQ$ and a curve of the form $y = x ^{ n }( n >1)$. If the area of the region taken away by the farmer $F_2$ by the farmer $F_2$ is eaxtly $30 \%$ of the area of $\triangle P Q R$, then the value of $n$ is. . . . . .

The area of figure bounded by $y = {e^x},\,y = {e^{ - x}}$ and the straight line $x = 1$ is

Solution of the differential equation $y' = y\tan x - 2\sin x,$ is

The graph of the function $y = f(x)$ is symmetrical about the line $x = 2$, then

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one iten is chosen ar random, the probability that it is rusted or is nail is