Derive the system (7) in the special case when $n = 3$ . [Hint: To determine the last equation, require that $I . [y_{p}] = g$ and use the fact that $y_{1}, y_{2}$ , and satisfy the corresponding homogeneous equation.]

Question

Derive the system (7) in the special case when $n = 3$ . [Hint: To determine the last equation, require that $I . [y_{p}] = g$ and use the fact that $y_{1}, y_{2}$ , and satisfy the corresponding homogeneous equation.]

Accepted Answer

The three functions $V_{1}, V_{2}$ and $V_{3}$ that satisfy the systems are given as;

$V_{1}^{'} y_{1} + V_{2}^{'} y_{2} + V_{3}^{'} y_{3} = 0 V_{1}^{'} y_{1}^{'} + V_{2}^{'} y_{2}^{'} + V_{3}^{'} y_{3}^{'} = 0 V_{1}^{'} y_{1}^{''} + V_{2}^{'} y_{2}^{''} + V_{3}^{'} y_{3}^{''} = g .$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Derive the system (7) in the special case when $n = 3$ . [Hint: To determine the last equation, require that $I . [y_{p}] = g$ and use the fact that $y_{1}, y_{2}$ , and satisfy the corresponding homogeneous equation.]

Step by Step Solution

Step 1: Determine the three unknown function

Step 2: Determine the solution by using three equations.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Derive the system (7) in the special case when n = 3. [Hint: To determine the last equation, require that I.[yp]=g and use the fact that y1,y2, and satisfy the corresponding homogeneous equation.]

Step by Step Solution

Step 1: Determine the three unknown function

Step 2: Determine the solution by using three equations.

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Derive the system (7) in the special case when $n = 3$ . [Hint: To determine the last equation, require that $I . [y_{p}] = g$ and use the fact that $y_{1}, y_{2}$ , and satisfy the corresponding homogeneous equation.]