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Cauchy’s linear differential equation  can be reduced to a linear differential equation with constant coefficient by using substitution
  • a)
    x = ez
  • b)
    y = ez
  • c)
    z = ex
  • d)
    z = ey
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Cauchy’s linear differential equationcan be reduced to a linear ...
Concept:
Any linear equation of the following form:
is considered as Cauchy’s differential equation. The equation has variable coefficients so its solution becomes tedious but we can convert the above equation into the linear differential equation with constant coefficients
By taking,
log x = z or x = ez
Proof:
log x = z
Taking differentiation on both sides we get,



Now, it can be solved by finding C.F and P.I just like we solve linear differential equations with constant coefficients.
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Most Upvoted Answer
Cauchy’s linear differential equationcan be reduced to a linear ...
Concept:
Any linear equation of the following form:
is considered as Cauchy’s differential equation. The equation has variable coefficients so its solution becomes tedious but we can convert the above equation into the linear differential equation with constant coefficients
By taking,
log x = z or x = ez
Proof:
log x = z
Taking differentiation on both sides we get,



Now, it can be solved by finding C.F and P.I just like we solve linear differential equations with constant coefficients.
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Cauchy’s linear differential equationcan be reduced to a linear differential equation with constant coefficient by using substitutiona)x = ezb)y = ezc)z = exd)z = eyCorrect answer is option 'A'. Can you explain this answer?
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