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Differential Equations
A bowl of water has a temperature of 50◦C. It is put into a refrigerator where the temperature is 5◦C. After 0.5 hours, the water is stirred and its temperature is measured to be 20◦C. It is then left to cool further, take t in Newton’s law of cooling to be measured in minutes. Use Newton’s law of cooling to predict when the temperature will be 10◦C.
Differential Equations
Find the solution of the initial-value problem and determine its interval of existence (i.e domain of the resulting function y).
(i) dy
dt = 1+t2
t ; y(t = 1) = 0:
Differential Equations
Verify that the given family of functions solves the differential equation.
dy/dt = (1-2t) y² , y = 1 / (C - t + t² )
dy/dt = y² sin(t) , y = 1 / (C +cos(t))
dy/dt = (1-2t) y² , y = 1 / (C - t + t² )
dy/dt = y² sin(t) , y = 1 / (C +cos(t))
Differential Equations
A particle is projected vertically upward with a velocity of 15 m/s from the point O. Find
the:
(i) maximum height reached.
(ii) time taken for it to return to O.
(iii) time taken for it to be 25 m below O.
the:
(i) maximum height reached.
(ii) time taken for it to return to O.
(iii) time taken for it to be 25 m below O.
Differential Equations
A bowl of water has a temperature of 50◦C. It is put into a refrigerator where the temperature is 5◦C. After 0.5 hours, the water is stirred and its temperature is measured to be 20◦C. It is then left to cool further, take t in Newton’s law of cooling to be measured in minutes. Use Newton’s law of cooling to predict when the temperature will be 10◦C.
Differential Equations
Find the solution of the initial-value problem and determine its interval of existence (i.e domain of the resulting function y). (i) dy dt = 1+t2 t , (ii) (t + 1)dy y(t = 1) = 0. dt = 1−y, y(t = 0) = 3. [Hint: Let A = −(±e−C).]
Differential Equations
A bowl of water has a temperature of 50⁰C. It is put into a refrigerator where the temperature is 5⁰C. After 0.5 hours, the water is stirred and its temperature is measured to be
20⁰C. It is then left to cool further, take t in Newton's law of cooling to be measured in
minutes. Use Newton's law of cooling to predict when the temperature will be 10⁰C.
20⁰C. It is then left to cool further, take t in Newton's law of cooling to be measured in
minutes. Use Newton's law of cooling to predict when the temperature will be 10⁰C.
Differential Equations
Find the solution of the initial-value problem and determine its interval of existence (i.e domain of the resulting function y).
(i)dy/dt=(1+t²)/t , y(t = 1) = 0
(ii) (t + 1) dy/dt = 1- y , y(t = 0) = 3 [Hint: Let A = -(±e^(-c))]
Differential Equations
2. (a) A bowl of water has a temperature of 50◦C. It is put into a refrigerator where the temperature is 5◦C. After 0.5 hours, the water is stirred and its temperature is measured to be 20◦C. It is then left to cool further, take t in Newton’s law of cooling to be measured in minutes. Use Newton’s law of cooling to predict when the temperature will be 10◦C.
Differential Equations
1. (a) Find the solution of the initial-value problem and determine its interval of existence (i.e domain of the resulting function y).
(i)dy =1+t2, y(t=1)=0. dt t
(ii)(t+1)dy =1−y, y(t=0)=3. [Hint: LetA=−(±e−C).] dt
(i)dy =1+t2, y(t=1)=0. dt t
(ii)(t+1)dy =1−y, y(t=0)=3. [Hint: LetA=−(±e−C).] dt
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#339914 on Dec 2023
#339914 on Dec 2023