dy = y² + 2yt +t² – 2y – 2t – 1 dt a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation:

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2a. Find a change of variable that transforms the equation into an autonomous equation

change of variable:

new equation:

b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.

2. Consider the equation:
dy
= y? + 2yt +t2 – 2y – 2t – 1
dt
%D
a. Find a change of variable that transforms the equation into an autonomous equation
change of variable:
new equation:
b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term
behaviors of all the qualitatively different solutions for the new variable, and then for the original
equation.
Transcribed Image Text:2. Consider the equation: dy = y? + 2yt +t2 – 2y – 2t – 1 dt %D a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.
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