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Solve
Which of the following is the solution of above equation, when x = 0?
- a)Can be any constant
- b)Undefined
- c)Zero
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
SolveWhich of the following is the solution of above equation, when x ...
Concept:
The given equation is multiplied with x to make it a equation of Cauchy Euler type.
The given equation is of Cauchy Euler type. Cauchy Euler equation is homogenous linear equation with variable coefficient.
The given equation is multiplied with x to make it a equation of Cauchy Euler type.
The given equation is of Cauchy Euler type. Cauchy Euler equation is homogenous linear equation with variable coefficient.
They can be reduced to linear equations with constant coefficients
Calculation:
Given:
Put x = et
log x = t
The given equation is written as
[x2D2 + xD]y = 0 ---(1)
Put xD = D’, x2D2 = D’(D’ - 1)
[D’(D’ - 1) + D’]y = 0
D’2 y = 0
The auxiliary equation is D’2 = 0
The roots of this equation are 0, 0
C.F = (At + B) e0t
y = (At + B)
Put t = log x
y = A log x + B
At x = 0; y is undefined as log 0 is undefined.
Most Upvoted Answer
SolveWhich of the following is the solution of above equation, when x ...
Concept:
The given equation is multiplied with x to make it a equation of Cauchy Euler type.
The given equation is of Cauchy Euler type. Cauchy Euler equation is homogenous linear equation with variable coefficient.
The given equation is multiplied with x to make it a equation of Cauchy Euler type.
The given equation is of Cauchy Euler type. Cauchy Euler equation is homogenous linear equation with variable coefficient.
They can be reduced to linear equations with constant coefficients
Calculation:
Given:
Put x = et
log x = t
The given equation is written as
[x2D2 + xD]y = 0 ---(1)
Put xD = D’, x2D2 = D’(D’ - 1)
[D’(D’ - 1) + D’]y = 0
D’2 y = 0
The auxiliary equation is D’2 = 0
The roots of this equation are 0, 0
C.F = (At + B) e0t
y = (At + B)
Put t = log x
y = A log x + B
At x = 0; y is undefined as log 0 is undefined.
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SolveWhich of the following is the solution of above equation, when x = 0?a)Can be any constantb)Undefinedc)Zerod)1Correct answer is option 'B'. Can you explain this answer?
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