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If y1(x) and y2(x) are solutions of y" + x2y' - (1 - x) y = 0 such that y1(0) = 0 ,y1'(0 ) = -1 and y2(0) = - 1, y2' (0) = 1, then the Wronskian W(y1, y2) on R
  • a)
    is never zero
  • b)
    is identically zero
  • c)
    is zero only at finite number of points
  • d)
    is zero at countable infinite number of points
Correct answer is option 'A'. Can you explain this answer?
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If y1(x) and y2(x) are solutions of y" + x2y - (1 - x) y = 0such ...
If y1(x) and y2(x) are solutions of y''(x) + p(x)y'(x) + q(x)y(x) = 0, then any linear combination of y1(x) and y2(x) is also a solution of the same differential equation.

In other words, if c1 and c2 are any constants, then the function y(x) = c1y1(x) + c2y2(x) is also a solution of y''(x) + p(x)y'(x) + q(x)y(x) = 0.

This property is known as the principle of superposition and is a fundamental concept in the theory of linear differential equations. It allows us to find a general solution by taking linear combinations of known solutions.
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If y1(x) and y2(x) are solutions of y" + x2y - (1 - x) y = 0such that y1(0) = 0 ,y1(0 ) = -1 and y2(0) = - 1, y2 (0) =1, then the Wronskian W(y1, y2) on Ra)is never zerob)is identically zeroc)is zero only at finite number of pointsd)is zero at countable infinite number of pointsCorrect answer is option 'A'. Can you explain this answer?
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If y1(x) and y2(x) are solutions of y" + x2y - (1 - x) y = 0such that y1(0) = 0 ,y1(0 ) = -1 and y2(0) = - 1, y2 (0) =1, then the Wronskian W(y1, y2) on Ra)is never zerob)is identically zeroc)is zero only at finite number of pointsd)is zero at countable infinite number of pointsCorrect answer is option 'A'. 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 If y1(x) and y2(x) are solutions of y" + x2y - (1 - x) y = 0such that y1(0) = 0 ,y1(0 ) = -1 and y2(0) = - 1, y2 (0) =1, then the Wronskian W(y1, y2) on Ra)is never zerob)is identically zeroc)is zero only at finite number of pointsd)is zero at countable infinite number of pointsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y1(x) and y2(x) are solutions of y" + x2y - (1 - x) y = 0such that y1(0) = 0 ,y1(0 ) = -1 and y2(0) = - 1, y2 (0) =1, then the Wronskian W(y1, y2) on Ra)is never zerob)is identically zeroc)is zero only at finite number of pointsd)is zero at countable infinite number of pointsCorrect answer is option 'A'. Can you explain this answer?.
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