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34. If a, b, andc are all positive constants and y(x) is a solutionof the differential equation ay" by' + cy 0, show thatimyx)0

Question
34. If a, b, andc are all positive constants and y(x) is a solution
of the differential equation ay" by' + cy 0, show that
imyx)0
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34. If a, b, andc are all positive constants and y(x) is a solution of the differential equation ay" by' + cy 0, show that imyx)0

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Step 1

Given that the differential equation is

ay" by' +cy = 0
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ay" by' +cy = 0

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Step 2

Write the corresponding auxiliary equation as,

ат" + bm + с %3D0
-btb-4ac
m=
2a
-b-b-4ac
-b+Nb-4ac and m
т,
2a
2a
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ат" + bm + с %3D0 -btb-4ac m= 2a -b-b-4ac -b+Nb-4ac and m т, 2a 2a

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Step 3

Substitute the values of m in the gener...

У(х)-се"* + се"т
-b+yb-4ac
у (х) -се
-b--4ае
+Cе
2а
2а
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У(х)-се"* + се"т -b+yb-4ac у (х) -се -b--4ае +Cе 2а 2а

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Tagged in

Math

Calculus

Differential Equations

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