112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(T) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3
112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(T) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 9E: Find the general solution for each differential equation. Verify that each solution satisfies the...
Related questions
Question
100%
Show all work, thank you! (Question 114 and 96)
![Explorations and Challenges
112-115. Functions from higher derivatives Find the function F that satisfies
the following differential equations and initial conditions.
112. F(x) = 1; F'(0) = 3, F(0)
= 4
113. F(x) = cos x; F'(0) = 3, F(π) = 4
114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3
115. F(x) = 672x5 +24x; F(0) = 0, F'(0) = 2, F(0) = 1
116. Mass on a spring A mass oscillates up and down on the end of a spring.
Find its positions relative to the equilibrium position if its acceleration is
a(t) = 2 sin t and its initial velocity and position are v(0) = 3 and
s(0) = 0, respectively.
117. Flow rate A large tank is filled with water when an outflow valve is opened
0. Water flows out at a rate, in gal/min, given by
Q'(t) = 0.1(100 – t²), for 0 ≤ t ≤ 10.
at t =
ank oftor &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ea0963c-64ff-46a6-b97c-79944ef211ae%2F751ec4f0-ead4-4ab0-81dd-0b4411e63086%2F1y5550q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Explorations and Challenges
112-115. Functions from higher derivatives Find the function F that satisfies
the following differential equations and initial conditions.
112. F(x) = 1; F'(0) = 3, F(0)
= 4
113. F(x) = cos x; F'(0) = 3, F(π) = 4
114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3
115. F(x) = 672x5 +24x; F(0) = 0, F'(0) = 2, F(0) = 1
116. Mass on a spring A mass oscillates up and down on the end of a spring.
Find its positions relative to the equilibrium position if its acceleration is
a(t) = 2 sin t and its initial velocity and position are v(0) = 3 and
s(0) = 0, respectively.
117. Flow rate A large tank is filled with water when an outflow valve is opened
0. Water flows out at a rate, in gal/min, given by
Q'(t) = 0.1(100 – t²), for 0 ≤ t ≤ 10.
at t =
ank oftor &
![91-96. Velocity to position Given the following velocity functions of an object
moving along a line, find the position function with the given initial position.
91. v(t) = 2t + 4; s(0) = 0
92. v(t) = et + 4; s(0) = 2
93. v(t) = 2√t; s(0) = 1
94. v(t) = 2 cos t; s(0) = 0
95. v(t) = 6t² + 4t − 10; s(0) = 0
96. v(t) = 4t + sin t; s(0) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ea0963c-64ff-46a6-b97c-79944ef211ae%2F751ec4f0-ead4-4ab0-81dd-0b4411e63086%2F6dpu7v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:91-96. Velocity to position Given the following velocity functions of an object
moving along a line, find the position function with the given initial position.
91. v(t) = 2t + 4; s(0) = 0
92. v(t) = et + 4; s(0) = 2
93. v(t) = 2√t; s(0) = 1
94. v(t) = 2 cos t; s(0) = 0
95. v(t) = 6t² + 4t − 10; s(0) = 0
96. v(t) = 4t + sin t; s(0) = 0
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,