Solution Found!
ami (a) A simple model for the shape of a tsunami, or
Chapter 3, Problem 19E(choose chapter or problem)
Tsunami (a) A simple model for the shape of a tsunami is given by
\(\frac{d W}{d x}=W \sqrt{4-2 W}\)
where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point off-shore. By inspection, find all constant solutions of the DE.
(b) Solve the differential equation in part (a). A CAS may be useful for integration.
(c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition W(0) = 2.
Text Transcription:
\(\frac{d W}{d x}=W \sqrt{4-2 W}\)
Questions & Answers
QUESTION:
Tsunami (a) A simple model for the shape of a tsunami is given by
\(\frac{d W}{d x}=W \sqrt{4-2 W}\)
where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point off-shore. By inspection, find all constant solutions of the DE.
(b) Solve the differential equation in part (a). A CAS may be useful for integration.
(c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition W(0) = 2.
Text Transcription:
\(\frac{d W}{d x}=W \sqrt{4-2 W}\)
ANSWER:Solution:Step 1:In this problem, we need to solve the differential equation of tsunami and we have to find the constant solution of the differential equation.