?For each of the following problems, verify that the given function is a solution to the

Chapter 7, Problem 9

(choose chapter or problem)

For each of the following problems, verify that the given function is a solution to the differential equation. Use a graphing utility to graph the particular solutions for several values of \(c_{1}\) and \(c_{2}\). What do the solutions have in common?

[T] \(y^{\prime \prime}+14 y^{\prime}+49 y=0 ; \quad y(x)=c_{1} e^{-7 x}+c_{2} x e^{-7 x}\)

Text Transcription:

y^{\prime \prime}+14 y^{\prime}+49 y=0 ; \quad y(x)=c_{1} e^{-7 x}+c_{2} x e^{-7 x}