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Alex Ar [27]
3 years ago
11

The given family of functions is the general solution of the differential equation on the indicated interval.Find a member of th

e family that is a solution of the initial-value problem.
y=c1+c2cosx+c3sinx,(−[infinity],[infinity]) y=c 1 +c 2 cosx+c 3 sinx,(−[infinity],[infinity])
y'''+y′=0,y(π)=0,y′(π)=2,y''(π)=−1 y +y =0,y(π)=0,y ′ (π)=2,y ′′ (π)=−1
Engineering
1 answer:
Alja [10]3 years ago
5 0

Answer:

Explanation:

y'''+y=0---(i)

General solution

y=c_1e^o^x+c_2\cos x +c_3 \sin x\\\\\Rightarrow y=c_1+c_2 \cos x+c_3 \sin x---(ii)\\\\y(\pi)=0\\\\\Rightarrow 0=c_1+c_2\cos (\pi)+c_3\sin (\pi)\\\\\Rightarrow c_1-c_2=0\\\\c_1=c_2---(iii)

y'=-c_2\cos x+c_3\cosx\\\\y'(\pi)=2\\\\\Rightarrow2=-c_2\sin(\pi)+c_3\cos(\pi)\\\\\Rightarrow-c_2(0)+c_3(-1)=2\\\\\Rightarrow c_3=-2\\\\y''-c_2\cos x -c_3\sin x\\\\y''(\pi)=-1\\\\\Rightarrow-1=-c_2 \cos (\pi)=c_3\sin(\pi)\\\\\Rightarrow-1=c_2-0\\\\\Rightarrow c_2=-1

in equation (iii)

c_1=c_2=-1

Therefore,

\large\boxed{y=-1-\cos x-2\sin x}

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Answer:

Hello some parts of your question is missing below is the missing part

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Explanation:

Given data :

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Hence total rate of heat loss

=  22 + 22.83

= 44.83 watts

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