1. (Slope fields) Sketch the slope field to the differential equation dy dr =-y+5 2. (Verify Solution) Verify that the function y(x) = 5-e is a solution to the differential equation dy dx dy dx = y + 5. 3. (Separation of Variables) Use separation of variables to determine the most general solution to the differential equation = sin(x)y.
1. (Slope fields) Sketch the slope field to the differential equation dy dr =-y+5 2. (Verify Solution) Verify that the function y(x) = 5-e is a solution to the differential equation dy dx dy dx = y + 5. 3. (Separation of Variables) Use separation of variables to determine the most general solution to the differential equation = sin(x)y.
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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Transcribed Image Text:1. (Slope fields) Sketch the slope field to the differential equation
dy
d.x
= y +5
2. (Verify Solution) Verify that the function y(x) = 5-e is a solution to the differential equation
dy
dx
dy
da
=-y + 5.
3. (Separation of Variables) Use separation of variables to determine the most general solution to the differential
equation
= sin(x)y.
Expert Solution
Step 1
To sketch a slope field we find the value of the slope for points in xy plane and make arrows with the slope calculated at those points. The resulting plot is called slope field of a differential equation.
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