Question

(a) For what values of $r$ does the function $y=e^{r x}$ satisfy the differential equation $2 y^{\prime \prime}+y^{\prime}-y=0 ?(b)$ if $r_{1}$ and $r_{2}$ are the values of $r$ that you found in part (a), show that every member of the family of functions $y=a e^{r_{1} x}+b e^{r_{2} x}$ is also a solution.

Name: a for what values of r does the function yer x satisfy the differential equation 2 yprime primeyprime y0 b if r1 and r2 are the values of r that you found in part a show that every member of the fam
Uploaded: 2021-03-15T23:43:32-08:00
Duration: 5 min 56 s
Channel: Bryan Lynn
Description: a for what values of r does the function yer x satisfy the differential equation 2 yprime primeyprime y0 b if r1 and r2 are the values of r that you found in part a show that every member of the fam

          (a) For what values of $r$ does the function $y=e^{r x}$ satisfy the differential equation $2 y^{\prime \prime}+y^{\prime}-y=0 ?(b)$ if $r_{1}$ and $r_{2}$ are the values of $r$ that you found in part (a), show that every member of the family of functions $y=a e^{r_{1} x}+b e^{r_{2} x}$ is also a solution.

Added by Joshua C.

Calculus: Early Transcendentals, Metric Edition

James Stewart, Daniel K. Clegg, Saleem… 9th Edition

Chapter 9

Instant Answer

Solved by Expert Bryan Lynn

03/15/2021

Step 1

The first derivative is $y' = re^{rx}$ and the second derivative is $y'' = r^2e^{rx}$. Show more…

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(a) For what values of $r$ does the function $y=e^{r x}$ satisfy the differential equation $2 y^{\prime \prime}+y^{\prime}-y=0 ?(b)$ if $r_{1}$ and $r_{2}$ are the values of $r$ that you found in part (a), show that every member of the family of functions $y=a e^{r_{1} x}+b e^{r_{2} x}$ is also a solution.