The differential equation y,+3= sinx is Select the correct answer a. first order

Question

The differential equation y,+3= sinx is Select the correct answer a. first order linear b. second order linear c. third order linear d. first order nonlinear e. second order nonlinear 2) The solution ofthe initial value problem y, = 2y+1.)(-1)=1/2 is y=-x/2-1/4+ce2x , where c= Select the correct answer. a. c. The initial value problem y' = />2-16, y(h) =y, has a unique solution guarantee Theorem 1.1 if: (Select the correct answer). 0 A b. c. The temperature of a cup of coffee obeys Newton's law of cooling. The initial temperature of the coffee is 1400F and one minute later, it is 125. The ambient temperature of the room is 65F. If TU) represents the temperature of the coffee at th the correct differential equation for the temperature is: (Select the correct answer) a. dT -K7-140) dt dT d -r-65) None of the above c. d. 7-140) = e)

Explanation / Answer

1. Option b second order linear differential equation

2. On substitution of x and y values in the solution we'd get

5e2/4 which is approx 1.25e2 on rounding off it will be close to e2 hence option C.

3. Option d because for every other option y' will be zero or negative.

4. None of the above, the formula for Newton's cooling

Is dT/dt= -k (T-To) where To is the room temperature.

Thus option, none of the above.

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