(a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential equation y dy = 5x to find an implicit solution of the initial-value dx problem y dy - 5x, y(3) = -9. dx Then sketch the graph of the explicit solution of this problem. y y 20 20- 10 10 (-9, 3) - 20 -10 10 20 -20 -10 10 20 (3, -9) 10- -10 -20 -20 y 20 20 10 10 \(-9, 3) - 20 - 10 10 20 -20 -10 10 20 (3, -9) F10 -10 -20 -20 Give the interval I of definition of the explicit solution. (Enter your answer using interval notation.) (b) Are there any explicit solutions of y dy = 5x that pass through the origin? (If dx yes, enter the explicit solutions as a comma-separated list. If not, enter NONE.) y =
(a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential equation y dy = 5x to find an implicit solution of the initial-value dx problem y dy - 5x, y(3) = -9. dx Then sketch the graph of the explicit solution of this problem. y y 20 20- 10 10 (-9, 3) - 20 -10 10 20 -20 -10 10 20 (3, -9) 10- -10 -20 -20 y 20 20 10 10 \(-9, 3) - 20 - 10 10 20 -20 -10 10 20 (3, -9) F10 -10 -20 -20 Give the interval I of definition of the explicit solution. (Enter your answer using interval notation.) (b) Are there any explicit solutions of y dy = 5x that pass through the origin? (If dx yes, enter the explicit solutions as a comma-separated list. If not, enter NONE.) y =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the
differential equation y Y = 5x to find an implicit solution of the initial-value
problem y
oy = 5x, y(3) = -9.
dx
Then sketch the graph of the explicit solution of this problem.
y
20
20
10
10-
(-9, 3)
-20
-10
10
20
-20
-10
10
20
(3, -9)
-10
10-
- 20
-20
y
20-
20
10
10
(-9, 3)
- 20
-10
10
20
-20
-10
10
20
(3, -9)
10
-10
-20
Give the interval I of definition of the explicit solution. (Enter your answer
using interval notation.)
(b) Are there any explicit solutions of y dy
= 5x that pass through the origin? (If
yes, enter the explicit solutions as a comma-separated list. If not, enter
NONE.)
y =
10
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