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Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y' + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] then
- a)It vanishes for any x ∈ [a, b]
- b)it does not vanish only at x = a
- c)it does not vanish for any x ∈ [a, b]
- d)it does not vanish only at x = b
Correct answer is option 'C'. Can you explain this answer?
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Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) an...
The Wronskian W[y1(x), y2(x)] is defined as the determinant of the matrix formed by taking the derivatives of the functions y1(x) and y2(x) with respect to x.
If y1(x) and y2(x) are solutions of the differential equation y'' + p(x)y' + q(x)y = 0, then the Wronskian satisfies the following equation:
W[y1(x), y2(x)] = W[y1(x), y2(x)] = y1(x)y2'(x) - y1'(x)y2(x) = C
where C is a constant.
The Wronskian can be used to determine whether the solutions y1(x) and y2(x) are linearly independent. If the Wronskian is non-zero at any point x, then the solutions are linearly independent and form a fundamental set of solutions. If the Wronskian is identically zero for all x, then the solutions are linearly dependent.
The Wronskian can also be used to find the general solution to a homogeneous linear differential equation. If the Wronskian is non-zero, then the general solution can be expressed as:
y(x) = c1*y1(x) + c2*y2(x)
where c1 and c2 are arbitrary constants.
If y1(x) and y2(x) are solutions of the differential equation y'' + p(x)y' + q(x)y = 0, then the Wronskian satisfies the following equation:
W[y1(x), y2(x)] = W[y1(x), y2(x)] = y1(x)y2'(x) - y1'(x)y2(x) = C
where C is a constant.
The Wronskian can be used to determine whether the solutions y1(x) and y2(x) are linearly independent. If the Wronskian is non-zero at any point x, then the solutions are linearly independent and form a fundamental set of solutions. If the Wronskian is identically zero for all x, then the solutions are linearly dependent.
The Wronskian can also be used to find the general solution to a homogeneous linear differential equation. If the Wronskian is non-zero, then the general solution can be expressed as:
y(x) = c1*y1(x) + c2*y2(x)
where c1 and c2 are arbitrary constants.
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Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer?
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Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect 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 W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect 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 W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer?.
Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect 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 W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect 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 W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer?.
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Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] thena)It vanishes for any x ∈ [a, b]b)it does not vanish only at x = ac)it does not vanish for any x ∈ [a, b]d)it does not vanish only at x = bCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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