%3D Solve the initival value problem: / = -8 cos(2a)/(6+5y), y(0) = -1.
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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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![a. Solve the initival value problem: y = -8 cos(2x)/(6+ 5y), y(0) = –1.
y =
(V1-40 sin(2x) -6)
b. When solving an ODE, the solution is only valid in some interval. Furthermore, if an initial condition is given, the solution will only be
valid in the largest interval in the domain of the solution that is around the x-value given in the initial condition.
In this case, since y(0) = –1, then the solution is only valid in the largest interval in the domain of y around x =
= 0.
For the following question, you do not need to find the interval exactly, but you should use a graphing utility, such as WolframAlpha,
to plot the solution.
Determine where the solution attains its maximum value. That is, you must compute the critical value of y using calculus. Note that
there is only one x-value in the largest interval about x = 0 that works, which you can determine based on the graph.
TC
Xcrit
%3D
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8c30dd-8618-4d51-9f32-993bb170f9da%2F0f8aa4af-8dc8-49ca-8c3b-7013716d5bbb%2Fd0lca5s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a. Solve the initival value problem: y = -8 cos(2x)/(6+ 5y), y(0) = –1.
y =
(V1-40 sin(2x) -6)
b. When solving an ODE, the solution is only valid in some interval. Furthermore, if an initial condition is given, the solution will only be
valid in the largest interval in the domain of the solution that is around the x-value given in the initial condition.
In this case, since y(0) = –1, then the solution is only valid in the largest interval in the domain of y around x =
= 0.
For the following question, you do not need to find the interval exactly, but you should use a graphing utility, such as WolframAlpha,
to plot the solution.
Determine where the solution attains its maximum value. That is, you must compute the critical value of y using calculus. Note that
there is only one x-value in the largest interval about x = 0 that works, which you can determine based on the graph.
TC
Xcrit
%3D
4.
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