Query 05

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course Mth 279

6/23 11

Query 05 Differential Equations*********************************************

Question: 3.2.6. Solve y ' + e^y t = e^y sin(t) with initial condition y(0) = 0.

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Your solution:

y' + e^y t = e^y * sin(t)

y'(t) = (e^y)sin(t) - (e^y)t

dy/dt = e^y(sin(t) - t)

int(dy/e^y) = int(sin(t) - t)dt

-e^-y = c - cos(t) - t^2/2

y(t) = -ln((1/2)t^2 + cos(t) - c)

y(0) = 0

0 = -ln((1/2)(0)^2 + cos(0) - c)

0 = ln(1)

(1/2)(0)^2 + cos(0) - c = 1

c = 0

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Self-critique rating:

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Question: 3.2.10. Solve 3 y^2 y ' + 2 t = 1 with initial condition y(0) = -1.

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Your solution:

3 y^2 dy = (1 - 2 t) dt

integrating yields

y^3 = t - t^2 + c

y = (t - t^2 + c) ^ (1/3)

substitute initial condition

y(0) = -1

-1 = (0 - 0^2 + c)^(1/3)

c = -1

y = (t - t^2 - 1)^(1/3)

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Self-critique rating:

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Question: 3.2.18. State a problem whose implicit solution is given by y^3 + t^2 + sin(y) = 4, including a specific initial

condition at t = 2.

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Your solution:

y^3 + t^2 + sin(y) = 4

y^3 + sin(y) = 4 - t^2

d/dy ( y^3 + sin(y)) = d/dt(4 - t^2)

y'(3y^2 + cos(y)) = -2t

y' = (-2t)/(3y^2 + cos(y))

Checking the intial condition.

y(2) = 0

0 = 4 - t^2

0 = 4 - 2^2

0 = 4 - 4

0 = 0

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Self-critique rating:

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Question: 3.2.24. Solve the equation y ' = (y^2 + 2 y + 1) sin(t) fand determine the t interval over which he solution

exists.

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Your solution:

y ' = (y^2 + 2*y + 1) * sin(t)

int(dy/(y^2 + 2*y + 1)) = int(sin(t))dt

int(y+1)^-2 dy = -cos(t) + c

-1/(y+1) = -cos(t) + c

-1 = (-cos(t))(y + 1)

y + 1 = -1/(-cos(t))

y = 1/(cos(t) + c) - 1

The solution exists everywhere except: cos(t) + c = 0

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Self-critique rating:

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Question: 3.2.28. Match the graphs of the solution curves with the equations y ' = - y^2, y ' = y^3 an dy ' = y ( 4 - y).

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Your solution:

I could locate any graphs in this assignment

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Self-critique rating:"

&#Very good work. Let me know if you have questions. &#