Factoring Differential

Calculus Level 2

Given \[y''+y'=2y\]

Where \(y=e^{rx}\). And \(r\) has two distinct values (the above equation has two solutions). Find the smallest value of \(r\)

Clarification

  • \(y'\) denotes the first derivative of \(y\) with respect to \(x\)
  • \(y''\) denotes the second derivative of \(y\) with respect to \(x\)
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