(See Solution) Step 9 of the method for solving a homogeneous equation says that, if the characteristic equation has one real root (r), the solution will be


Question: Step 9 of the method for solving a homogeneous equation says that, if the characteristic equation has one real root \((r)\), the solution will be \(x=A e^{r t}+B t e^{r t}\). Differentiate this solution to show that it is the correct one.

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