The solution of , ( dy dx ) = ax + by is - Vidyadip

MCQ

The solution of $\log \,\left( {\frac{{dy}}{{dx}}} \right) = ax + by$ is

A
$\frac{{{e^{by}}}}{b} = \frac{{{e^{ax}}}}{a} + c$
✓
$\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$
C
$\frac{{{e^{ - by}}}}{a} = \frac{{{e^{ax}}}}{b} + c$
D
None of these

✓

Answer

Correct option: B.

$\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$

b
(b) $\log \left( {\frac{{dy}}{{dx}}} \right) = ax + by$ ==> $\frac{{dy}}{{dx}} = {e^{ax + by}} = {e^{ax}}.{e^{by}}$

==> ${e^{ - by}}dy = {e^{ax}}dx$ ==> $\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A=\left(a_1, a_2\right)$ and $B=\left(b_1, b_2\right)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$ ?

Let $A_1,A_2,........A_{11}$ are players in a team with their T-shirts numbered $1,2,.....11$. Hundred gold coins were won by the team in the final match of the series. These coins is to be distributed among the players such that each player gets atleast one coin more than the number on his T-shirt but captain and vice captain get atleast $5$ and $3$ coins respectively more than the number on their respective T-shirts, then in how many different ways these coins can be distributed ?

The sum of the abosolute maximum and minimum values of the function $f(x)=\left|x^2-5 x+6\right|-3 x+2$ in the interval $[-1,3]$ is equal to :

$\int_0^{\pi /2} {{e^x}\sin x\,dx = } $

Let the first term $a$ and the common ratio $r$ of a geometric progression be positive integers. If the sum of its squares of first three terms is $33033$, then the sum of these three terms is equal to

If the normal to the ellipse $3x^2 + 4y^2 = 12$ at a point $P$ on it is parallel to the line, $2x + y = 4$ and the tangent to the ellipse at $P$ passes through $Q(4, 4)$ then $PQ$ is equal to

${d \over {dx}}\left( {{1 \over {{x^4}\sec x}}} \right) = $

If $g:[ - 2,\,2] \to R$ where $g(x) = $ ${x^3} + \tan x + \left[ {\frac{{{x^2} + 1}}{P}} \right]$ is a odd function then the value of parametric $P$ is

The circular wire of diameter $10\,cm$ is cut and placed along the circumference of a circle of diameter $1\, metre.$ The angle subtended by the wire at the centre of the circle is equal to

If $\overrightarrow{ x }$ and $\overrightarrow{ y }$ be two non$-$zero vectors such that $|\overrightarrow{ x }+\overrightarrow{ y }|=|\overrightarrow{ x }|$ and $2 \overrightarrow{ x }+\lambda \overrightarrow{ y }$ is perpendicular to $\overrightarrow{ y },$ then the value of $\lambda$ is