Consider the following differential equation. 2y''+y'-y=0 For what values of r does the function y = e^{rx} satisfy the equation?

Haven

Haven

Answered question

2021-05-16

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

Answer & Explanation

Aubree Mcintyre

Aubree Mcintyre

Skilled2021-05-18Added 73 answers

Step 1
Given,
Consider the following differential equation 2y''+y'-y=0 and y=erx.
Step 2
Now,
y=erx
Differentiating on both sides, we get
y=d(erx)dx
y=erxd(rx)dx
y=erxr
Again, differentiating on both sides, we get
y=rd(erx)dx
y=r2erx
2y+yy=0
2r2erx+rerxerx=0
2r2+r1=0
2r2+2rr1=0
2r(r+1)1(r+1)=0
(2r1)(r+1)=0
Either 2r-1=0 or r+1 = 0
r=12orr=1
The value of r is 12 and -1.

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