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Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations if
  • a)
    ad = bc
  • b)
    ac = bd
  • c)
    ad ≠ bc
  • d)
    ac ≠ bd
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let y1(x) and y2(x) be linearly independent solution of the differenti...
y3(x) and y4(x) are linearly dependent if y3(x) = ky4(x) where k is any constant 

Since, y1(x) and y2(x) are independent
So, a - kc = 0
and b - kd = 0
or 
So, y3(x) and y4(x) are independent if

implies ad ≠ bc
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Most Upvoted Answer
Let y1(x) and y2(x) be linearly independent solution of the differenti...
It seems like your question is incomplete. Could you please provide the complete differential equation?
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Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations ifa)ad = bcb)ac = bdc)ad ≠ bcd)ac ≠ bdCorrect answer is option 'C'. Can you explain this answer?
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Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations ifa)ad = bcb)ac = bdc)ad ≠ bcd)ac ≠ bdCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations ifa)ad = bcb)ac = bdc)ad ≠ bcd)ac ≠ bdCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations ifa)ad = bcb)ac = bdc)ad ≠ bcd)ac ≠ bdCorrect answer is option 'C'. Can you explain this answer?.
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