A direction field for the differential equation y' = cos(y) – sin(x) is given %3D below. a) Sketch the graph of the solutions that satisfies the given initial condition y(0) = 1 on the direction field. %3D 3.0

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Chapter2: Second-order Linear Odes
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Please guide me on how to solve this differential equation. I'm not good with direction field. Thank you for your help
A direction field for the differential equation y' = cos(y) – sin(x) is given
%3D
below.
a) Sketch the graph of the solutions that satisfies the given initial
condition y(0) = 1 on the direction field.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4
-3
-2
4
b) State one point where the direction field is shown to be increasing.
c) State one point where the direction field is shown to be decreasing.
d) Evaluate the exact value of the slope at the point (5).
Transcribed Image Text:A direction field for the differential equation y' = cos(y) – sin(x) is given %3D below. a) Sketch the graph of the solutions that satisfies the given initial condition y(0) = 1 on the direction field. 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4 -3 -2 4 b) State one point where the direction field is shown to be increasing. c) State one point where the direction field is shown to be decreasing. d) Evaluate the exact value of the slope at the point (5).
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