Question
Write an equivalent first-order differential equation and initial condition for $y .$$y=x+4+\int_{-2}^{x} t e^{y(t)} d t$
Step 1
The derivative of $y$ is $y'$, the derivative of $x$ is 1, the derivative of 4 is 0, and by the Fundamental Theorem of Calculus, the derivative of $\int_{-2}^{x} t e^{y(t)} d t$ is $x e^{y(x)}$. So we get: \[y'=1+x e^{y}\] Show more…
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