The Laplace transform method reduces a differential equation of order n problem

Question

The Laplace transform method reduces a differential equation of order n problem to

A differential equation of order n-1 problem.

Characteristic polynomial of a degree n problem.

A homogeneous differential problem.

Step 1. Compute the Laplace transform of f (t). Step 2. Compute the inverse transform of step 1. The result is

F(s)

F-1(s)

f(t)

f-1(t)

F-1(f(t))

The formula for the Laplace transform of the integral of a function is a consequence of

The Fundamental Theorem of Arithmetic.

The Fundamental Theorem of Algebra.

The Fundamental Theorem of Calculus.

The Fundamental Theorem of Laplace Transforms.

The Fundamental Theorem of Differential equations.

Integration by parts is a formula for finding the integral of

Any product.

Any sum.

Certain products.

Certain sums.

Partial fractions

The method of partial fractions mostly involves

Trig functions.

Exponential functions.

Logarithmic functions

Rational functions

None of the above

Question 1.1.

The Laplace transform method reduces a differential equation of order n problem to

(Points : 1)       A calculus problem.
      An algebra problem.
      

A differential equation of order n-1 problem.

      

Characteristic polynomial of a degree n problem.

      

A homogeneous differential problem.

Question 2.2.

Step 1. Compute the Laplace transform of f (t). Step 2. Compute the inverse transform of step 1. The result is

(Points : 1)       

F(s)

      

F-1(s)

      

f(t)

      

f-1(t)

      

F-1(f(t))

Question 3.3.

The formula for the Laplace transform of the integral of a function is a consequence of

(Points : 1)       

The Fundamental Theorem of Arithmetic.

      

The Fundamental Theorem of Algebra.

      

The Fundamental Theorem of Calculus.

      

The Fundamental Theorem of Laplace Transforms.

      

The Fundamental Theorem of Differential equations.

Question 4.4.

Integration by parts is a formula for finding the integral of

(Points : 1)       

Any product.

      

Any sum.

      

Certain products.

      

Certain sums.

      

Partial fractions

Question 5.5.

The method of partial fractions mostly involves

(Points : 1)       

Trig functions.

      

Exponential functions.

      

Logarithmic functions

      

Rational functions

      

None of the above

Explanation / Answer

The Laplace transform method reduces a differential equation of order n problem to An algebra problem.

Compute the Laplace transform of f (t). Step 2. Compute the inverse transform of step 1. The result is f(t)

The formula for the Laplace transform of the integral of a function is a consequence of The Fundamental Theorem of Calculus.

Integration by parts is a formula for finding the integral of Any product.

The method of partial fractions mostly involves Rational functions

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