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If P(y) and Q(x) are arbitrary functions of y and a respectively, then the differential equation P(y)dx+ Q(x)dy = 0
  • a)
    Is never exact
  • b)
    Is exact if P(y) = ey and Q(x) = ex
  • c)
    Is exact only if P(y) = Ay + B and Q(x) = Ax + C, A, B, C being constants
  • d)
    Is always exact
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If P(y) and Q(x) are arbitrary functions of y and a respectively, then...
Proof : The given differential equation is
P(y)dx+Q(x)dy = 0 ...(i)
Comparing (i) with
Mdx + Ndy= 0 ...(ii)
M = P(y) and N = Q(x)
Differential equation (i) will be exact if and only if

    ...(iii)
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Most Upvoted Answer
If P(y) and Q(x) are arbitrary functions of y and a respectively, then...
Proof : The given differential equation is
P(y)dx+Q(x)dy = 0 ...(i)
Comparing (i) with
Mdx + Ndy= 0 ...(ii)
M = P(y) and N = Q(x)
Differential equation (i) will be exact if and only if

    ...(iii)
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If P(y) and Q(x) are arbitrary functions of y and a respectively, then the differential equation P(y)dx+ Q(x)dy = 0a)Is never exactb)Is exact if P(y) = ey and Q(x) = exc)Is exact only if P(y) = Ay + B and Q(x) = Ax + C, A, B, C being constantsd)Is always exactCorrect answer is option 'C'. Can you explain this answer?
Question Description
If P(y) and Q(x) are arbitrary functions of y and a respectively, then the differential equation P(y)dx+ Q(x)dy = 0a)Is never exactb)Is exact if P(y) = ey and Q(x) = exc)Is exact only if P(y) = Ay + B and Q(x) = Ax + C, A, B, C being constantsd)Is always exactCorrect 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 If P(y) and Q(x) are arbitrary functions of y and a respectively, then the differential equation P(y)dx+ Q(x)dy = 0a)Is never exactb)Is exact if P(y) = ey and Q(x) = exc)Is exact only if P(y) = Ay + B and Q(x) = Ax + C, A, B, C being constantsd)Is always exactCorrect 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 If P(y) and Q(x) are arbitrary functions of y and a respectively, then the differential equation P(y)dx+ Q(x)dy = 0a)Is never exactb)Is exact if P(y) = ey and Q(x) = exc)Is exact only if P(y) = Ay + B and Q(x) = Ax + C, A, B, C being constantsd)Is always exactCorrect answer is option 'C'. Can you explain this answer?.
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