APFIVE Particular Solution to a Differential Equation
If $$y=g(x)$$ is a solution to the differential equation $$\frac{dy}{dx}=\cos(e^x)$$ with the initial condition $$g(0)=-1$$, which of the following is true?
A
$$g(x)=\cos(e^x)$$
B
$$g(x)=-1+\int_0^x\cos(e^t)\, dt$$
C
$$g(x)=-\sin(e^x)$$
D
$$g(x)=\int_0^x\cos(e^t)\, dt$$
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