26. The quartics c²y² = x(x - a)³ with a held fixed.
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
Please answer number 26
Transcribed Image Text:23. The confocal central conics
b²+d
with a and b held fixed.
ANS. (xy' y)(yy' + x) = (a² − b²)y'.
ANS. 2x(x a)y' = y(3x − 2a).
25. The cubics of exercise 24 with c held fixed and a to be eliminated.
24. The cubics cy² = x²(x − a) with a held fixed.
28. The strophoids y² :
=
a² + a
29. The cissoids v²
+
1
ANS. 2cy(xy' - y) = x³.
26. The quartics c²y² = x(x − a)³ with a held fixed. ANS. 2x(x a)y' = y(4x − a).
27. The quartics of exercise 26 with c held fixed and a to be eliminated.
-
ANS. c²(2xy' y)³ = 27x4y.
ANS. (x4 4x²y² − y4) dx + 4x³y dy = 0.
x²(a + x)
ax
-
-
ANS. 2x³y = y(y² + 3x²).
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