The general solution of the differential equa | vedclass

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

Question

(C) Given the differential equation: $\frac{dy}{dx} = \frac{3e^{2x} + 3e^{4x}}{e^x + e^{-x}}$Simplify the numerator by factoring out $3e^{2x}$: $3e^{2

Vedclass · Accepted Answer

$y = e^{3x} + c$,where $c$ is a constant of integration.

Vedclass · Answer

(C) Given the differential equation: $\frac{dy}{dx} = \frac{3e^{2x} + 3e^{4x}}{e^x + e^{-x}}$Simplify the numerator by factoring out $3e^{2x}$: $3e^{2x}(1 + e^{2x})$Simplify the denominator: $e^x + e^{-x} = e^x + \frac{1}{e^x} = \frac{e^{2x} + 1}{e^x}$Substitute these back into the equation: $\frac{dy}{dx} = \frac{3e^{2x}(1 + e^{2x})}{\frac{e^{2x} + 1}{e^x}}$Cancel the common term $(1 + e^{2x})$: $\frac{dy}{dx} = 3e^{2x} \cdot e^x = 3e^{3x}$Integrate both sides with respect to $x$: $\int dy = \int 3e^{3x} dx$$y = 3 \cdot \frac{e^{3x}}{3} + c = e^{3x} + c$

The general solution of the differential equation $\frac{dy}{dx} = \frac{3e^{2x} + 3e^{4x}}{e^x + e^{-x}}$ is

Similar Questions

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is

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

Find the general solution of the differential equation: $\frac{dy}{dx} = (1+x^2)(1+y^2)$

The solution of the differential equation $\frac{dy}{dx} = e^{x-y} + x^2e^{-y}$ is...

$A$ particle moves in a straight line with a velocity given by $\frac{dx}{dt} = x + 1$ (where $x$ is the distance covered). The time taken by the particle to traverse a distance of $99 \ m$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module