The value of x ( 0.2 ) and y ( 0.2 ) with h = 0.1 for the differential equation x ′ = x + y and y ′ = x − y with the initial values x ( 0 ) = 1 and y ( 0 ) = 2 .

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Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

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Design a PDA recognizing each of the following languages and draw its state diagram. Note that the transition function must be in the format of “a, b →c", namely we can only push/pop one symbol into/from the stack one time upon one input symbol. You will receive 0 point if you push/pop multiple symbols into/from the stack one time upon one input symbol. (1) {w|wa"b", n is odd} = (2) {w|w=w², length of w is odd and Σ = {a,b} } (3) {w|w= = a²b²n, n ≥1 } (4) {w|w= =a^bn+mcm, n≥0, m ≥ 1 } (5) {w|w=a²b³n, n≥0} (6) {w|w= = a¹³, n ≥ 1, m≥ 1 and n‡m } Hint: two cases: n > m and n

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a. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?

Answer 2

Question

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

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Answer 3

Question

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

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Answer 4

Question

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

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Answer 5

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

Answer 6

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

Answer 7

Chapter 9, Problem 7RE

To determine

The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

Answer 8

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Answer 9

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Answer 11

The value of x ( 0.2 ) and y ( 0.2 ) with h = 0.1 for the differential equation x ′ = x + y and y ′ = x − y with the initial values x ( 0 ) = 1 and y ( 0 ) = 2 .

Solution Summary: The approximated solution for the first order linear differential equation is given as follows: lxprime

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The value of x(0.2) and y(0.2) with h=0.1 for the differential equation x′=x+y and y′=x−y with the initial values x(0)=1 and y(0)=2.

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