Consider the following differential equation. 2y+y-y=0

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Consider the following differential equation.  2y+y-y=0

Aubree Mcintyre · Accepted Answer

Step 1Given,Consider the following differential equation 2y&#039;&#039;+y&#039;-y=0 and y=erx.Step 2Now,y=erxDifferentiating on both sides, we get⇒y′=d(erx)dx⇒y′=erxd(rx)dx⇒y′=erxrAgain, differentiating on both sides, we get⇒y″=rd(erx)dx⇒y″=r2erx∴2y″+y′−y=0⇒2r2erx+rerx−erx=0⇒2r2+r−1=0⇒2r2+2r−r−1=0⇒2r(r+1)−1(r+1)=0⇒(2r−1)(r+1)=0Either 2r-1=0 or r+1 = 0r=12orr=−1∴ The value of r is 12 and -1.

Consider the following differential equation. 2y+y-y=0

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