Verify that the solution to the initial value problem
$x' = 5 x - 3 y - 2; x (0) = 2, y' = 4 x - 3 y - 1; y (0) = 0$
Satisfies $| x (t) | + | y (t) | \to + \infty$ as $t \to + \infty$

Question

Verify that the solution to the initial value problem
$x' = 5 x - 3 y - 2; x (0) = 2, y' = 4 x - 3 y - 1; y (0) = 0$
Satisfies $| x (t) | + | y (t) | \to + \infty$ as $t \to + \infty$

Accepted Answer

The solutions for the given initial value problem are $x (t) = - \frac{5}{4} e^{- t} + \frac{9}{4} c_{2} e^{3 t} + 1$

and $y (t) = - \frac{5}{2} e^{- t} + \frac{3}{2} e^{3 t} + 1$ . Then, it satisfies the $\underset{t \to \infty}{l i m} (|x (t)| + |y (t)|) = \infty$ also.

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Verify that the solution to the initial value problem
$x' = 5 x - 3 y - 2; x (0) = 2, y' = 4 x - 3 y - 1; y (0) = 0$
Satisfies $| x (t) | + | y (t) | \to + \infty$ as $t \to + \infty$

Step by Step Solution

Step 1: General form

Step 2: Evaluate the given equation

Step 3: Substitution method

Step 4: Find the initial value problem

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Verify that the solution to the initial value problemx'=5x-3y-2; x0=2,y'=4x-3y-1; y0=0Satisfies |xt|+|yt|→+∞ as t→+∞

Step by Step Solution

Step 1: General form

Step 2: Evaluate the given equation

Step 3: Substitution method

Step 4: Find the initial value problem

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Verify that the solution to the initial value problem
$x' = 5 x - 3 y - 2; x (0) = 2, y' = 4 x - 3 y - 1; y (0) = 0$
Satisfies $| x (t) | + | y (t) | \to + \infty$ as $t \to + \infty$