xy" – (y)³ – y' = 0. Exercises In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Ans. y dx- x dy 0. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. Ans. (y- k) dx - (x h) dy = 0. 3. Straight lines with slope and y-intercept equal. 4, Straight lines with slope and x-intercept equal. 5. Straight lines with algebraic sum of the intercepts fixed as k. y dx - (x + 1) dy 0. Ans. (y')? = xy- y. Ans. Ans. (xy'yXy-1) + ky' = 0. 6. Straight lines at a fixed distance p from the origin. 7. Circles with center at the origin. 8. Circles with center on the x-axis. 9. Circles with fixed radius r and tangent to the x-axis. Ans. (xy' y) = p?[1 + (y)]. Ans. x dx + y dy = 0. Ans. yy" + (y)? + 1 0. %3D Ans. (y t r)(y')? + y? + 2ry 0.
xy" – (y)³ – y' = 0. Exercises In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. Ans. y dx- x dy 0. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. Ans. (y- k) dx - (x h) dy = 0. 3. Straight lines with slope and y-intercept equal. 4, Straight lines with slope and x-intercept equal. 5. Straight lines with algebraic sum of the intercepts fixed as k. y dx - (x + 1) dy 0. Ans. (y')? = xy- y. Ans. Ans. (xy'yXy-1) + ky' = 0. 6. Straight lines at a fixed distance p from the origin. 7. Circles with center at the origin. 8. Circles with center on the x-axis. 9. Circles with fixed radius r and tangent to the x-axis. Ans. (xy' y) = p?[1 + (y)]. Ans. x dx + y dy = 0. Ans. yy" + (y)? + 1 0. %3D Ans. (y t r)(y')? + y? + 2ry 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Kindly answer item no. 9
![xy" – (y')³ – y' = 0.
Exercises
In each exercise, obtain the differential equation of the family of plane curves
described and sketch several representative members of the family.
Ans. y dx- x dy = 0.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
3. Straight lines with slope and y-intercept equal.
4, Straight lines with slope and x-intercept equal.
5. Straight lines with algebraic sum of the intercepts fixed as k.
Ans. (y- k) dx - (x h) dy = 0.
y dx - (x + 1) dy 0.
Ans. (y')? = xy - y.
Ans.
Ans. (xy'-yXy-1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
9. Circles with fixed radius r and tangent to the x-axis.
Ans. (xy' y) = p²[1+ (y)].
Ans. x dx + y dy = 0.
Ans. yy" + (y)² + 1 = 0.
%3D
Ans. (y t r)(y')? + y? + 2ry 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4848a09c-86dc-44c2-8280-8974eb986c52%2F14d61b8c-00d6-4b01-8337-8d7ee953bfee%2Frs5udk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:xy" – (y')³ – y' = 0.
Exercises
In each exercise, obtain the differential equation of the family of plane curves
described and sketch several representative members of the family.
Ans. y dx- x dy = 0.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
3. Straight lines with slope and y-intercept equal.
4, Straight lines with slope and x-intercept equal.
5. Straight lines with algebraic sum of the intercepts fixed as k.
Ans. (y- k) dx - (x h) dy = 0.
y dx - (x + 1) dy 0.
Ans. (y')? = xy - y.
Ans.
Ans. (xy'-yXy-1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
9. Circles with fixed radius r and tangent to the x-axis.
Ans. (xy' y) = p²[1+ (y)].
Ans. x dx + y dy = 0.
Ans. yy" + (y)² + 1 = 0.
%3D
Ans. (y t r)(y')? + y? + 2ry 0.
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