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Asked Oct 24, 2019

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One solution of the differential equation y" +y' = O is y = e. Use Reduction of Order to find a second
linearly independent solution.
O y e
Оу-хе*
Оу-ех
O y c
Оу-ех
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One solution of the differential equation y" +y' = O is y = e. Use Reduction of Order to find a second linearly independent solution. O y e Оу-хе* Оу-ех O y c Оу-ех

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Step 1

In such problems ie second order linear differential equations when we are given one solution,y1 we assume the second solution to be of the form, y2=vy1 and substitute y2 in the given ode and reduce order of the differential equation by using the fact that y1 is a solution.

Compute:y2,y2’’

 

=-vev'e
= e (-v+v')
v)e* (-v'+v°)
= e" (v=v-v+v*)
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=-vev'e = e (-v+v') v)e* (-v'+v°) = e" (v=v-v+v*)

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Step 2

Substitute y2,y2’’ in given differential equation

 

e (v-2v'+v")+e"* (-v+v')=0
e(-vv)0
-v'v 0
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e (v-2v'+v")+e"* (-v+v')=0 e(-vv)0 -v'v 0

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Step 3

Let u=v’ we get a first order dif...

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