Particular Solution of a Differential Equation

Question

Let $$y=f(x)$$ be the particular solution to the differential equation $$\frac{dy}{dx}=e^{\sin(x)}$$ with the initial condition $$f(\frac{\pi}{2})=1$$. Which of the following is true?

Accepted Answer

$$f(x)=1+\int_{\pi/2}^xe^{\sin(t)}\, dt$$

Answer

$$f(x)=\cos(x)e^{\sin(x)}$$

Answer

$$f(x)=e^{\sin(x)}$$

Answer

$$f(x)=1+\int_0^xe^{\sin(t)}\, dt$$

Particular Solution of a Differential Equation

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