Question

solve the ivp by using the laplace transform

y1' = -y2 , y1 = y2'

y1(0)=1 , y2(0)=-1

Answer #1

1)using the laplace transform, solve the initial value
problem
y1'+y2=0
y1+y2'=2cost
y1(0)=1,y2(0)=0
2)using the convolution, find the inverse transform
of (a) F(s)=1/s(s-1) and (b) G(s)=5/(s^2+1)(s^2+25)

Solve the IVP. Using the Laplace transform.
y'' - (r1+r2)y' +
r1r2y = Aeat , y(0)=0, y'(0)=0

Use
Laplace transform to solve IVP
2y”+2y’+y=2t , y(0)=1 , y’(0)=-1

Use the definition of the Laplace transform to solve the
IVP:
4y''− 4y' + 5y = δ(t), y(0) = −1, y'(0) = 0.

Use the Laplace transform to solve the IVP:
y′(t) +y(t) = cos(t),
y(0) = 0.

Use laplace transform to solve the given IVP
y''-2y'-48y=0
y(0)=13
y'(0)=6

Use the Laplace transform to solve the following IVP
y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2,
where δ(t) is the Dirac delta function.

Given the differential equation
y''−2y'+y=0, y(0)=1, y'(0)=2
Apply the Laplace Transform and solve for Y(s)=L{y}
Y(s) =
Now solve the IVP by using the inverse Laplace Transform
y(t)=L^−1{Y(s)}
y(t) =

solve using the laplace transform y''-2y'+y=e^-t , y(0)=0 ,
y'(0)=1

y^''-y^'-2y= e^t , y(0)=0 and y^'(0)=1
Solve by using laplace transform

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