Save Determine whether the given function is a solution to the given differential equation. de e-2e"-3, + 40 = -6e 3t dt. The function @=2e - e is not a solution to the differential equation - de 0-+40 = -6e 3t because when 2 .4. 3t
Save Determine whether the given function is a solution to the given differential equation. de e-2e"-3, + 40 = -6e 3t dt. The function @=2e - e is not a solution to the differential equation - de 0-+40 = -6e 3t because when 2 .4. 3t
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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Determine whether the given function is a solution to the given differential equation.
de
e=2e4-3t
dr?
0-
+ 40 = -6 e 3t
dt
.....
The function 0 = 2 e 4t - e 3t is not a solution to the differential equation
de
+ 40 = -6 e 3t, because when 2 e 4t - e 3t is substituted for 0,
de
-0-
di?
is substituted for
and
is substituted for
the two sides of the differential equation
dt
dt
are not equivalent on any intervals of t.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55b17e19-b284-43b9-956b-c8e36fd9a8ae%2F1fc1433a-6eb5-4b25-93bb-b2bae19675c3%2Fyq963gf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Save
Determine whether the given function is a solution to the given differential equation.
de
e=2e4-3t
dr?
0-
+ 40 = -6 e 3t
dt
.....
The function 0 = 2 e 4t - e 3t is not a solution to the differential equation
de
+ 40 = -6 e 3t, because when 2 e 4t - e 3t is substituted for 0,
de
-0-
di?
is substituted for
and
is substituted for
the two sides of the differential equation
dt
dt
are not equivalent on any intervals of t.
![Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation.
30x y' +2 (y')3 sin y- 10 (y')2
2 sin y+ 5xy - x° = 9, y'" =
6x° - 5y
.....
4
30x"y' +2 (y')3 sin y – 10 (y')²
a solution to the differential equation.
equivalent to y'' =
Therefore, 2 sin y+ 5xy-x° = 9
which
Applying implicit differentiation to the equation gives
6x -5y
(Type an equation.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55b17e19-b284-43b9-956b-c8e36fd9a8ae%2F1fc1433a-6eb5-4b25-93bb-b2bae19675c3%2F3ffvao7f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation.
30x y' +2 (y')3 sin y- 10 (y')2
2 sin y+ 5xy - x° = 9, y'" =
6x° - 5y
.....
4
30x"y' +2 (y')3 sin y – 10 (y')²
a solution to the differential equation.
equivalent to y'' =
Therefore, 2 sin y+ 5xy-x° = 9
which
Applying implicit differentiation to the equation gives
6x -5y
(Type an equation.)
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