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(dy)/(dx) -y =e^(x ) " when" x=0 and y=1...

`(dy)/(dx) -y =e^(x ) " when" x=0 and y=1`

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To solve the differential equation \(\frac{dy}{dx} - y = e^{x}\) with the initial condition \(y(0) = 1\), we will follow these steps: ### Step 1: Identify the type of differential equation This is a first-order linear differential equation of the form: \[ \frac{dy}{dx} + P(x)y = Q(x) \] where \(P(x) = -1\) and \(Q(x) = e^{x}\). ...
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