The solution of the differential equation fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $x - y = v$. Then,differentiating with respect to $x$,we get $1 - \frac{dy}{dx} = \frac{dv}{dx}$,which implies $\frac{dy}{dx} = 1 - \frac{dv}{

Vedclass · Accepted Answer

$2(x - y) + \log(x - y + 2) = x + c$

Vedclass · Answer

(C) Let $x - y = v$. Then,differentiating with respect to $x$,we get $1 - \frac{dy}{dx} = \frac{dv}{dx}$,which implies $\frac{dy}{dx} = 1 - \frac{dv}{dx}$.Substituting this into the given differential equation: $1 - \frac{dv}{dx} = \frac{v + 3}{2v + 5}$.Rearranging the terms: $\frac{dv}{dx} = 1 - \frac{v + 3}{2v + 5} = \frac{2v + 5 - v - 3}{2v + 5} = \frac{v + 2}{2v + 5}$.Separating the variables: $\int \frac{2v + 5}{v + 2} dv = \int dx$.Simplifying the integrand: $\int \left( 2 + \frac{1}{v + 2} \right) dv = \int dx$.Integrating both sides: $2v + \log|v + 2| = x + c$.Substituting $v = x - y$ back into the equation: $2(x - y) + \log|x - y + 2| = x + c$.

The solution of the differential equation $\frac{dy}{dx} = \frac{x - y + 3}{2(x - y) + 5}$ is

Similar Questions

The first formed primary phloem is referred to as $A$. The later formed primary phloem is referred to as $B$.
Choose the correct combination of $A$ and $B$.

$A$ weak acid $HX$ has the dissociation constant $1 \times 10^{-5} \ M$. It forms a salt $NaX$ on reaction with alkali. The percentage hydrolysis of $0.1 \ M$ solution of $NaX$ is ........ $\%$.

Which one of the following population interactions is widely used in medical science for the production of antibiotics?

$A$ ball of mass $160\, g$ is thrown up at an angle of $60^\circ$ to the horizontal at a speed of $10\, m\,s^{-1}$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly ........ $kg\, m^2/s$ $(g = 10\, m\,s^{-2})$.

Which of the following orders is correct for the heat of hydrogenation of these compounds?

Vedclass Test Series

Exam Paper Generator

Online Exam Module