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) Given the differential equation: $\frac{dy}{dx} = ae^{bx} + c\cos mx$ Separate the variables: $dy = (ae^{bx} + c\cos mx) dx$ Integrate both sides

Vedclass · Accepted Answer

$y = \frac{ae^{bx}}{b} + \frac{c}{m}\sin mx + k$

Vedclass · Answer

(C) Given the differential equation: $\frac{dy}{dx} = ae^{bx} + c\cos mx$ Separate the variables: $dy = (ae^{bx} + c\cos mx) dx$ Integrate both sides with respect to their variables: $\int dy = \int (ae^{bx} + c\cos mx) dx$ Applying the integration rules $\int e^{bx} dx = \frac{e^{bx}}{b}$ and $\int \cos(mx) dx = \frac{\sin(mx)}{m}$: $y = \frac{ae^{bx}}{b} + \frac{c\sin(mx)}{m} + k$,where $k$ is the constant of integration.

The solution of the differential equation $\frac{dy}{dx} = (ae^{bx} + c\cos mx)$ is

Similar Questions

Find a particular solution of the differential equation $(x-y)(dx+dy)=dx-dy$ given that $y=-1$ when $x=0$. (Hint: put $x-y=t$)

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

The general solution of the differential equation $e^{\frac{1}{2}\left(\frac{dy}{dx}\right)}=3^x$ is (where $C$ is a constant of integration).

The solution of the differential equation $x dy - y dx = 0$ represents:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module