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If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal to
- a)(−2, −2)
- b)(−2, −1)
- c)(−1, −2)
- d)(−1, −1)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If xhyk is an integrating factor of the differential equation y(1 + xy...
If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal to (−2, −2)
This question is part of UPSC exam. View all IIT JAM courses
Most Upvoted Answer
If xhyk is an integrating factor of the differential equation y(1 + xy...
Xy) dy = 0, then we have:
xhyk(1-xy) dx + yhyk(1-xy) dy = 0
Dividing both sides by (1-xy), we get:
xhyk dx + yhyk dy = 0
This is a homogeneous differential equation, which can be solved by the substitution y = vx. We have:
y' = v'x + v
y' = (xv)' (chain rule)
Substituting y = vx and y' = (xv)', we get:
xhv'x + xhv = 0
Dividing both sides by xh^2, we get:
v' + v/h = 0
This is a linear first-order differential equation, which has an integrating factor of e^(integral of 1/h dx). Therefore, the integrating factor of the original differential equation is:
e^(integral of 1/h dx)
where h = (1-xy).
xhyk(1-xy) dx + yhyk(1-xy) dy = 0
Dividing both sides by (1-xy), we get:
xhyk dx + yhyk dy = 0
This is a homogeneous differential equation, which can be solved by the substitution y = vx. We have:
y' = v'x + v
y' = (xv)' (chain rule)
Substituting y = vx and y' = (xv)', we get:
xhv'x + xhv = 0
Dividing both sides by xh^2, we get:
v' + v/h = 0
This is a linear first-order differential equation, which has an integrating factor of e^(integral of 1/h dx). Therefore, the integrating factor of the original differential equation is:
e^(integral of 1/h dx)
where h = (1-xy).
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If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer?
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If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer?.
If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer?.
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