Question 3: Let c be an arbitrary constant, and consider the equation: 2c3 3 y = c²x- Show that the equation above is a solution to the differential equation y = xy' - ²²(y')³/2 Now, show that the equation y = x³/3 is also a solution to the differential equation above. Seem- ingly, we can find first order differential equations whose solutions are not characterized by a one parameter family of functions. We will talk more about when and why this can happen on Thursday.
Question 3: Let c be an arbitrary constant, and consider the equation: 2c3 3 y = c²x- Show that the equation above is a solution to the differential equation y = xy' - ²²(y')³/2 Now, show that the equation y = x³/3 is also a solution to the differential equation above. Seem- ingly, we can find first order differential equations whose solutions are not characterized by a one parameter family of functions. We will talk more about when and why this can happen on Thursday.
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:Question 3: Let c be an arbitrary constant, and consider the equation:
2c³
y = c²x-
3
Show that the equation above is a solution to the differential equation
y = x - (y^³/2
Now, show that the equation y = x³/3 is also a solution to the differential equation above. Seem-
ingly, we can find first order differential equations whose solutions are not characterized by a
one parameter family of functions. We will talk more about when and why this can happen on
Thursday.
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