In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. ANS. (y ANS. y dx - x 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. ANS. 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. 10. Circles tangent to the x-axis. - k) dx − (x − h) dy = 0. y dx - (x + 1) dy = 0. ANS. (y)² = xy' — y. ANS. (xy' — y)(y' − 1) + ky' = 0. - 6. Straight lines at a fixed distance p from the origin. ANS. (xy' - y)² = p²[1 + (y′)²]. ANS. x dx + y dy = 0. ANS. yy" + (y)² + 1 = 0. ANS. (y ± r)²(y')² + y² ± 2ry = 0. ANS. [1 + (y')²]³ = [yy″ + 1 + (y')²]².
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. ANS. (y ANS. y dx - x 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. ANS. 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. 10. Circles tangent to the x-axis. - k) dx − (x − h) dy = 0. y dx - (x + 1) dy = 0. ANS. (y)² = xy' — y. ANS. (xy' — y)(y' − 1) + ky' = 0. - 6. Straight lines at a fixed distance p from the origin. ANS. (xy' - y)² = p²[1 + (y′)²]. ANS. x dx + y dy = 0. ANS. yy" + (y)² + 1 = 0. ANS. (y ± r)²(y')² + y² ± 2ry = 0. ANS. [1 + (y')²]³ = [yy″ + 1 + (y')²]².
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
100%
JUST SKETCH THE GRAPHS PLEASE. NOS. 1-10
![In each exercise, obtain the differential equation of the family of plane curves described
and sketch several representative members of the family.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
ANS. y dx x dy = 0.
ANS. (y — k) dx − (x − h) dy = 0.
-
ANS.
y dx
(x + 1) dy = 0.
(y)² = xy' — y.
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.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
ANS. (xy' — y)(y' − 1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
ANS.
9. Circles with fixed radius r and tangent to the x-axis.
ANS.
10. Circles tangent to the x-axis.
ANS.
(xy' — y)² = p²[1 + (y')²].
ANS. x dx + y dy = 0.
ANS. yy" + (y')² + 1
=
: 0.
(y ± r)²(y')² + y² ± 2ry = 0.
ANS. [1 + (y')²]³ = [yy” + 1 + (y')²]².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8943d76e-c254-4322-8f39-c91cdf9301f3%2F5caa57d3-185b-4e58-9e73-9a79cdabce5c%2F1emx1qj_processed.png&w=3840&q=75)
Transcribed Image Text:In each exercise, obtain the differential equation of the family of plane curves described
and sketch several representative members of the family.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
ANS. y dx x dy = 0.
ANS. (y — k) dx − (x − h) dy = 0.
-
ANS.
y dx
(x + 1) dy = 0.
(y)² = xy' — y.
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.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
ANS. (xy' — y)(y' − 1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
ANS.
9. Circles with fixed radius r and tangent to the x-axis.
ANS.
10. Circles tangent to the x-axis.
ANS.
(xy' — y)² = p²[1 + (y')²].
ANS. x dx + y dy = 0.
ANS. yy" + (y')² + 1
=
: 0.
(y ± r)²(y')² + y² ± 2ry = 0.
ANS. [1 + (y')²]³ = [yy” + 1 + (y')²]².
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
