First order Differential Equations

According to Newton’s law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. A substance initially at temperature 90°C is kept in moving air at temperature 26°C, the difference equation satisfied by temperature θ of substance at any time t is…

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Orthogonal trajectories of family of curves whose differential equation is , is ...

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The differential equation of orthogonal trajectories of family of curves is…

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If the differential equation of family of curves then its orthogonal trajectories is given by ....

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A body originally at 80°C cools down to 60°C in 20 minutes in a room where the temperature is 40°C. The differential equation by Newton’s law of cooling is then the value of k is…

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The differential equation of orthogonal trajectories of family of curves is…

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D) None of these

By Newton’s law of cooling the differential equation of body originally at 80°C cools down to 60°C in 20 minutes in surrounding temperature of 40°C is The temperature of the body after 40 minutes is…

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A) 60°C
B) 50°C
C) 35°C
D) 85°C

If the differential equation of family of rectangular hyperbola xy = c is x = -y then its orthogonal trajectories is ....

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Orthogonal trajectories of family of curves whose differential equation is , is ...

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B)
C)
D) None of these

The differential equation of orthogonal trajectories of family of curves is…

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B)
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D)

The differential equation of orthogonal trajectories of family of curves is…

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B)
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D)

Newton’s law of cooling states that….

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A) The temperature of a body changes at the rate which is proportional to the temperature of surrounding medium.
B) The temperature of a body changes at the rate which is inversely proportional to the difference in temperature between that of surrounding medium and that of body itself.
C) The temperature of a body changes at the rate which is proportional to the sum of temperatures of surrounding medium and that of body itself.
D) The temperature of a body changes at the rate which is proportional to the difference in temperature between that of surrounding medium and that of body itself.

Orthogonal trajectories of family of curves whose differential equation is , is ...

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B)
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D)

The differential equation of orthogonal trajectories of family of curves = is…

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A thermometer is taken outdoors where the temperature is 0°C, from a room in which the temperature is 21°C and temperature drops to 10°C in 1 minute. If the differential equation by Newton’s law of cooling is then temperature T of thermometer at time t is given by…

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If the differential equation of family of straight lines y = mx is = then its orthogonal trajectories is ...

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The temperature of the air is 30°C and the substance cools from 100°C to 70°C in 15 minutes. If differential equation by Newton’s law of cooling is then the value of k is…

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The differential equation of orthogonal trajectories of family of curves is…

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If is the temperature of the surrounding and is temperature of the body at any time t satisfies the differential equation then is given by…

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Suppose a corpse at a temperature of 32°C arrives at mortuary where the temperature is kept at 10°C. Then by Newton’s law of cooling the differential equation satisfied by temperature T of corpse t hours later is…

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A copper ball is heated to a temperature of 100°C and at time t = 0 it is placed in water which is maintained at 30°C. The temperature of the ball reduces to 70°C in 3 minutes. The differential equation by Newton’s law of cooling is

. Then the time required to reduce the temperature of ball to 31°C is…

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A) 3 min
B) 7.78 min
C) 22.78 min
D) 15.78 min

If the family of curves is given by then the differential equation of orthogonal trajectories of family is …

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D)

The differential equation of orthogonal trajectories of family of straight lines is…

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A body at temperature 100°C is placed in a room whose temperature is 20°C and cools to 60°C in 5 minutes. By Newton’s law of cooling the differential equation is . Then the temperature after 8 minutes is…

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A) 46.4°C
B) 64.4°C
C) 40.4°C
D) 20°C

The differential equation of orthogonal trajectories of family of curves is…

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B)
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First order Differential Equations : Question 1 of 25

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