dy Show that (x)=Ce3x-3 is a solution to dx +3y=-9 for any choice of the constant C. Thus, Ce 3x-3 is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes. Substitute (x) for y and find the derivative to substitute for dy dx +3y=-9 +3(Ce-3x-3) = -9 After using the dx property to rewrite 3 (Ce3x-3) as ☐, the left side of the equation simplifies to -9, showing that ((x) is indeed a solution for any value of C. Choose the graph that shows the correct curves for C=0, ±1, and ±2. O A. ○ C. CO Q Q C-2 -2 Q C d-o B. ○ D. C = 1-C2 CO G C-2 Q
dy Show that (x)=Ce3x-3 is a solution to dx +3y=-9 for any choice of the constant C. Thus, Ce 3x-3 is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes. Substitute (x) for y and find the derivative to substitute for dy dx +3y=-9 +3(Ce-3x-3) = -9 After using the dx property to rewrite 3 (Ce3x-3) as ☐, the left side of the equation simplifies to -9, showing that ((x) is indeed a solution for any value of C. Choose the graph that shows the correct curves for C=0, ±1, and ±2. O A. ○ C. CO Q Q C-2 -2 Q C d-o B. ○ D. C = 1-C2 CO G C-2 Q
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Please answer all parts to the following diff eq. problem:
Transcribed Image Text:dy
Show that (x)=Ce3x-3 is a solution to
dx
+3y=-9 for any choice of the constant C. Thus, Ce 3x-3 is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.
Substitute (x) for y and find the derivative to substitute for
dy
dx
+3y=-9
+3(Ce-3x-3)
= -9
After using the
dx
property to rewrite 3 (Ce3x-3) as ☐, the left side of the equation simplifies to -9, showing that ((x) is indeed a solution for any value of C.
Choose the graph that shows the correct curves for C=0, ±1, and ±2.
O A.
○ C.
CO
Q
Q
C-2
-2
Q
C
d-o
B.
○ D.
C = 1-C2
CO
G
C-2
Q
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