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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

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

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(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

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