Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in t u 1 − plane of equation d u 1 d t = − ( k 1 + k 2 ) u 1 + k 2 u 20 + k 1 T a , where k 1 , k 2 , u 20 and T a are constants.

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Answer 1

Question

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

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Answer 2

Question

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Expert Solution & Answer

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Answer 3

Question

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Expert Solution & Answer

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Answer 4

Question

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Expert Solution & Answer

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See solution

Answer 5

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Answer 6

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

Answer 7

Chapter 3.2, Problem 14P

(a)

To determine

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

Answer 8

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

Answer 9

(b)

To determine

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

Answer 10

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

Answer 11

(c)

To determine

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

Answer 12

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Answer 13

(d)

To determine

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in t u 1 − plane of equation d u 1 d t = − ( k 1 + k 2 ) u 1 + k 2 u 20 + k 1 T a , where k 1 , k 2 , u 20 and T a are constants.

Solution Summary: The author determines the critical points and classifies them as asymptotically stable or unstable. They also draw the phase line and several graphs of the solution in tu_1- plane

Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in $tu1−$ plane of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ , where $k1,k2,u20 and Ta$ are constants.

Thesolution of equation $du1dt=−(k1+k2)u1+k2u20+k1Ta$ subject to the initial condition $u1(0)=u10$ , where $k1,k2,u20 and Ta$ are constants. Use this solution to verify the qualitative result of part (a).

Thephysical interpretation of setting $ε=0$ and the equilibrium solution $u1=k2u20+k1Tak1+k2$ .

Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.

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Chapter 3 Solutions