Differential Equations - Exam 1

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What is the equation for Newton’s Law of Cooling?

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<p>(note: solutions for nodal source curve towards smaller/negative eigenspace vectors)</p>

(note: solutions for nodal source curve towards smaller/negative eigenspace vectors)

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<p><span style="background-color: transparent;">asymptotically stable</span></p>

asymptotically stable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p>unstable</p>

unstable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p>unstable</p>

unstable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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note also: u1 = (-2,1)

<p>note also: u1 = (-2,1)</p>
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note also: u1 = (1,-2)

<p>note also: u1 = (1,-2)</p>
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<p><span style="background-color: transparent;">every equilibrium is stable but not asymptoticall</span></p>

every equilibrium is stable but not asymptoticall

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p><span style="background-color: transparent;">every equilibrium is unstable</span></p>

every equilibrium is unstable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p><span style="background-color: transparent;">equilibrium asymptotically stable</span></p>

equilibrium asymptotically stable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p><span style="background-color: transparent;">equilibrium unstable</span></p>

equilibrium unstable

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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<p><span style="background-color: transparent;">equilibrium stable (not asymptotically)</span></p>

equilibrium stable (not asymptotically)

Describe the stability of the equilibrium

<p><span style="background-color: transparent;">Describe the stability of the equilibrium</span></p>
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