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densk [106]
2 years ago
14

Use the laplace transform to solve the initial value problem: y''+y=1, y(0)=2 and y'(0)=0

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
5 0

Answer:

y(s) = sin t + 2 cost

Step-by-step explanation:

given,

     y''  + y = 1,                       y(0) = 2  and  y'(0) = 0

applying Laplace transformation both side

s²y(s) - s y(o)- y'(0) + y(s) = L{1}

s²y(s) - 2 s + y(s)  = L{1}

y(s)(s² + 1 ) =  L{1}  + 2 s

y(s)= L^{-1}(\dfrac{L(1)}{s^2 + 1})+2L^{-1}(\dfrac{s}{s^2+1})

     y(s) = sin t + 2 cost

hence, the required solution of Laplace will be

     y(s) = sin t + 2 cost

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This question is easy if you think about it. First get the area of the rectangular part of the shape and then find area of the two semi-circles then add them together.

First, let's solve for the rectangle because it's easier.

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Now for the semi-circle. First use the equation for finding the area of a circle which is A = Pi * r^2. We'll use 3.14 for Pi.

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The figure is made of rectangular prisms. What is the volume?
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