Particular Solution to a Differential Equation

Question

Let $$y=g(x)$$ be the particular solution to the differential equation $$\frac{dy}{dx}=\cos(e^x)$$ that satisfies the initial condition $$g(0)=-1$$. Which of the following is an expression for $$g(x)$$?

Accepted Answer

$$g(x)=-1+\int_0^x\cos(e^t)\, dt$$

Answer

$$g(x)=\cos(e^x)$$

Answer

$$g(x)=\int_0^x\cos(e^t)\, dt$$

Answer

$$g(x)=-\sin(e^x)$$

Particular Solution to a Differential Equation

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