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The complementary function of the differential equation
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The complementary function of the differential equationa)b)c)d)Correct...
Concept:
Linear differential equations with variable coefficients can be reduced to linear differential equations with constant coefficients by suitable substitutions.
Euler Cauchy Homogeneous linear equation:

Calculation:
Given:
Euler Cauchy equation:

Put x = et
⇒ t = log x

Now the equation becomes,

Auxillary equation is D2 + 2D + 1 = 0
⇒ (D + 1)2 = 0
⇒ D = -1, -1
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Most Upvoted Answer
The complementary function of the differential equationa)b)c)d)Correct...
Concept:
Linear differential equations with variable coefficients can be reduced to linear differential equations with constant coefficients by suitable substitutions.
Euler Cauchy Homogeneous linear equation:

Calculation:
Given:
Euler Cauchy equation:

Put x = et
⇒ t = log x

Now the equation becomes,

Auxillary equation is D2 + 2D + 1 = 0
⇒ (D + 1)2 = 0
⇒ D = -1, -1
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The complementary function of the differential equationa)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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