Two linearly independent solutions of the homogeneous equation, x2y” + xy’ + y = 0 , area)x3/2, x-1/2b)x2, x2In xc)cos(In x), sin(In x)d)e-x cos(x), ex sin(x)Correct answer is option 'C'. Can you explain this answer?

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Two linearly independent solutions of the homogeneous equation, x²y” + xy’ + y = 0 , are

a)
x^3/2, x^-1/2
b)
x², x²In x
c)
cos(In x), sin(In x)
d)
e^-xcos(x), e^x sin(x)

Correct answer is option 'C'. Can you explain this answer?

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Practice Test: Electronics Engineering (ECE)- 13

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Two linearly independent solutions of the homogeneous equation, x2y” ...

x²y′′ + xy + y = 0

⇒(θ(θ − 1) + θ + 1)y = 0

⇒ (θ²− θ + θ + 1)y = 0

⇒ (θ²+ 1)y = 0

AE is m²+ 1 = 0

⇒ m = ±i

⇒ CF = C₁cos⁡z + C₂sin⁡z

∴ Solution is y = C₁cos(In x) + C₂ sin(In x)

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Two linearly independent solutions of the homogeneous equation, x2y” + xy’ + y = 0 , area)x3/2, x-1/2b)x2, x2In xc)cos(In x), sin(In x)d)e-x cos(x), ex sin(x)Correct answer is option 'C'. Can you explain this answer?

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Two linearly independent solutions of the homogeneous equation, x2y” + xy’ + y = 0 , area)x3/2, x-1/2b)x2, x2In xc)cos(In x), sin(In x)d)e-x cos(x), ex sin(x)Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two linearly independent solutions of the homogeneous equation, x2y” + xy’ + y = 0 , area)x3/2, x-1/2b)x2, x2In xc)cos(In x), sin(In x)d)e-x cos(x), ex sin(x)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two linearly independent solutions of the homogeneous equation, x2y” + xy’ + y = 0 , area)x3/2, x-1/2b)x2, x2In xc)cos(In x), sin(In x)d)e-x cos(x), ex sin(x)Correct answer is option 'C'. Can you explain this answer?.

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