Find the first three nonzero terms, or as many as exist, in the series expansion about x=0 for a general solution to the given equation for x>0. xy" + (1- x)y' -y = 0 The equation has a general solution in the form c,Y1 (x) + Csy2(x) where y, (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has a term with y, (x), then count that term as only one term. Y1() = D+ --- and y2(x) = D + -

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Find the first three nonzero terms, or as many as exist, in the series expansion about x= 0 for a general solution to the given equation for x>0.
ху" + (1- х)у' - у %3D0
The equation has a general solution in the form C, y, (x) + cay2(x) where y, (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has
term with y, (x), then count that term as
only one term.
y1(X) =+ .. and y2(x) =+ ..
Transcribed Image Text:Find the first three nonzero terms, or as many as exist, in the series expansion about x= 0 for a general solution to the given equation for x>0. ху" + (1- х)у' - у %3D0 The equation has a general solution in the form C, y, (x) + cay2(x) where y, (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has term with y, (x), then count that term as only one term. y1(X) =+ .. and y2(x) =+ ..
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