The solution of frac{dy}{dx} = e^x(sin x + co | vedclass

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Question

(C) Given the differential equation $\frac{dy}{dx} = e^x(\sin x + \cos x)$.Integrating both sides with respect to $x$,we get $y = \int e^x(\sin x + \c

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$y = e^x \sin x + c$

Vedclass · Answer

(C) Given the differential equation $\frac{dy}{dx} = e^x(\sin x + \cos x)$.Integrating both sides with respect to $x$,we get $y = \int e^x(\sin x + \cos x) dx$.We know the standard integral formula $\int e^x(f(x) + f'(x)) dx = e^x f(x) + c$.Here,let $f(x) = \sin x$,then $f'(x) = \cos x$.Substituting this into the formula,we get $y = e^x \sin x + c$.

The solution of $\frac{dy}{dx} = e^x(\sin x + \cos x)$ is

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