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Verify that y, and y, are solutions of the given differential equation but that y = c,y, + c,y, is, in general, not a solution. 1 yy" Cr')²; v1 = 4, Y2 = x² Y2Y2" = 2x2 Now let y = c,Y, + c,y2. Then we have the following. yy" = | 2C,C,x? 4CC2 +

Verify that y, and y, are solutions of the given differential equation but that y = c,y, + c,y, is, in general, not a solution. 1 yy" Cr')²; v1 = 4, Y2 = x² Y2Y2" = 2x2 Now let y = c,Y, + c,y2. Then we have the following. yy" = | 2C,C,x? 4CC2 +

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Verify that y1 and y2 are solutions of the given differential equation but that 
y = c1y1 + c2y2 is, in general, not a solution.
yy'' = 1/2(y' )2;  y1 = 4,  y2 = x2
Now let y = c1y1 + c2y2. Then we have the following.
yy"=
1/2(y' )2=
 
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Verify that y, and y, are solutions of the given differential equation but that y = c,Y1 + C,Y2 is, in general, not a solution. yy" =r')?; y1 = 4, Y2 = x? Y2Y2" = 2x2 Now let y = c,y, + c,y2. Then we have the following. |4C;C, + 2C,C,r² yy" = |2C,C,? yy" * r')?
Transcribed Image Text:Verify that y, and y, are solutions of the given differential equation but that y = c,Y1 + C,Y2 is, in general, not a solution. yy" =r')?; y1 = 4, Y2 = x? Y2Y2" = 2x2 Now let y = c,y, + c,y2. Then we have the following. |4C;C, + 2C,C,r² yy" = |2C,C,? yy" * r')?
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