fy that (x)= do dx 14ce7x (1-ce²x)² mplify your answer.) 14ce7x 2 1-ce7x stitute (x) for y and the derivative for dx dy = 7y²-14y - ce²x)2 dy where c is an arbitrary constant, is a one-parameter family of solutions to 2 mplify your answer.) - (-)-(-)) dy dx 2 1-ce7x _7y²-14y 2 expression on the right can be further simplified by using a Graph the solution curves corresponding to c= 0, +1, +2 using the same coordinate axes. dy of to subtract the fractions in the numerator, resulting in the same expression that was substituted for on the left. dx
fy that (x)= do dx 14ce7x (1-ce²x)² mplify your answer.) 14ce7x 2 1-ce7x stitute (x) for y and the derivative for dx dy = 7y²-14y - ce²x)2 dy where c is an arbitrary constant, is a one-parameter family of solutions to 2 mplify your answer.) - (-)-(-)) dy dx 2 1-ce7x _7y²-14y 2 expression on the right can be further simplified by using a Graph the solution curves corresponding to c= 0, +1, +2 using the same coordinate axes. dy of to subtract the fractions in the numerator, resulting in the same expression that was substituted for on the left. dx
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
options for first box are
a) partial fraction decomposition
b) rational root
c) common factor
d) common denominater
Transcribed Image Text:Verify that (x) =
Find
do
dx
do
dx
14ce7x
(1-ce²x)²
(Simplify your answer.)
=
2
dy
, where c is an arbitrary constant, is a one-parameter family of solutions to =
7x
dx
1- ce
dy
Substitute (x) for y and the derivative for dx
dy
dx
=
2
7y - 14y
2
2
2
2
= ²(₁-² ²- )* - ¹ (1 - ~^~^)
7
- 14
1-ce' 7x
1-ce7x
2
14ce7x
(1-ce²x) ²
(Simplify your answer.)
The expression on the right can be further simplified by using a
of
7y - 14y
2
Graph the solution curves corresponding to c = 0, ±1, ±2 using the same coordinate axes.
C
dy
to subtract the fractions in the numerator, resulting in the same expression that was substituted for
dx
on the left.
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