Question

We consider the following second order differential equation: d^2y / dt^2 = 5 dy / dt - 2.25y. (i) Write this equation as a system of two first order differential equations of the form: d / dt x = A * x, where x := <x1, x2>^T and A is a 2x2 matrix. The matrix A is equal to: (ii) The eigenvalues ?1, ?2 of the matrix A in ascending order (?1 ? ?2), are equal to: ?1 = ?2 = (iii) Write the corresponding eigenvectors (v1 corresponds to ?1 and v2 corresponds to ?2) in their simplest form, such as their first component is 1: v1 = (1, v2 = (1, (iv) The general solution of this second order differential equation has the form: y(t) = C1 + C2 , where C1, C2 are arbitrary complex numbers. The syntax for the exponential of x is exp(x). Please enter one answer only in each box (that is, don't enter two answers in one box). (v) The solution satisfying this second order differential equation and the initial conditions y(0) = 0, dy/dt(0) = -64 has: C1 = C2 =

          We consider the following second order differential equation:
d^2y / dt^2 = 5 dy / dt - 2.25y.
(i) Write this equation as a system of two first order differential equations of the form:
d / dt x = A * x,
where
x := <x1, x2>^T
and A is a 2x2 matrix. The matrix A is equal to:
(ii) The eigenvalues ?1, ?2 of the matrix A in ascending order (?1 ? ?2), are equal to:
?1 =
?2 =
(iii) Write the corresponding eigenvectors (v1 corresponds to ?1 and v2 corresponds to ?2) in their simplest form, such as their first component is 1:
v1 = (1,
v2 = (1,
(iv) The general solution of this second order differential equation has the form:
y(t) = C1 + C2 ,
where C1, C2 are arbitrary complex numbers.
The syntax for the exponential of x is exp(x). Please enter one answer only in each box (that is, don't enter two answers in one box).
(v) The solution satisfying this second order differential equation and the initial conditions y(0) = 0, dy/dt(0) = -64 has:
C1 =
C2 =

We consider the following second order differential equation:
d^2y / dt^2 = 5 dy / dt - 2.25y.
(i) Write this equation as a system of two first order differential equations of the form:
d / dt x = A * x,
where
x := <x1, x2>^T
and A is a 2x2 matrix. The matrix A is equal to:
(ii) The eigenvalues ?1, ?2 of the matrix A in ascending order (?1 ? ?2), are equal to:
?1 =
?2 =
(iii) Write the corresponding eigenvectors (v1 corresponds to ?1 and v2 corresponds to ?2) in their simplest form, such as their first component is 1:
v1 = (1,
v2 = (1,
(iv) The general solution of this second order differential equation has the form:
y(t) = C1 + C2 ,
where C1, C2 are arbitrary complex numbers.
The syntax for the exponential of x is exp(x). Please enter one answer only in each box (that is, don't enter two answers in one box).
(v) The solution satisfying this second order differential equation and the initial conditions y(0) = 0, dy/dt(0) = -64 has:
C1 =
C2 =

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