Use the Laplace transform to solve the following initial value
problem:
y^('')+10y^(')=0,y(0)=4,y^(')(0)=3
a. Using Y for the Laplace transform of y(t), i.e.,
Y=L{y(t)}, find the equation you get by taking the
Laplace transform of the differential equation
=0
b. Now solve for
Y(s)=
c. Write the above answer in its partial fraction
decomposition, Y(s)=(A)/(s+a)+(B)/(s+b) where Y(s)=y(t)=a
Y(s)=
d. Now by inverting the transform, find
y(t)=
Use the Laplace transform to solve the following initial value problem:
y"+10y=0
y(0) = 4, y(0) =3
a. Using Y for the Laplace transform of y(t), i.e.,
Y = C{y(t)}, find the equation you get by taking the Laplace transform of the differential equation
b. Now solve for
c. Write the above answer in its partial fraction A B decomposition, Y(s) where a< b s+a s+b
d. Now by inverting the transform, find
()h
