Question
Write an equivalent first-order differential equation and initial condition for $y .$$y=2-\int_{0}^{x}(1+y(t)) \sin t d t$
Step 1
The derivative of $y$ with respect to $x$ is $y'(x)$, and the derivative of the integral from $0$ to $x$ of $(1+y(t)) \sin t dt$ with respect to $x$ is $(1+y(x)) \sin x$ by the Fundamental Theorem of Calculus. So we have: \[y'(x) = (1+y(x)) \sin x\] Show more…
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