# Write an equivalent​ first-order differential equation and initial condition for

Write an equivalent​ first-order differential equation and initial condition for y.
$y=-1+{\int }_{0}^{x}\left(2t-5y\left(t\right)\right)dt$
What is the equivalent first-order differential equation?
${y}^{\prime }=?$
What is the initial condition?
$y\left({y}^{\prime }=?\right)=?$

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Elois Puryear
Given,
$y=-1+{\int }_{0}^{x}\left(2t-5y\left(t\right)\right)dt$
Differentiating both side, we get
${y}^{\prime }=0+2x-5y\left(x\right)$

Since, $y\left(x\right)=-1+{\int }_{0}^{x}\left(2t-5y\left(t\right)\right)dt$

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