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

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) = sin t + 2 cost

hence, the required solution of Laplace will be

     y(s) = sin t + 2 cost

what?

step-by-step explanation:

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: