In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.
$x - d^{2} y / d t^{2} = t + 1$
$d x / d t + d y / d t - 2 y = e^{t}$

Question

In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.
$x - d^{2} y / d t^{2} = t + 1$
$d x / d t + d y / d t - 2 y = e^{t}$

Accepted Answer

The general solution is $x (t) = \frac{- 3 c_{1} - \sqrt{7} c_{2}}{2} e^{- \frac{t}{2}} \cos \frac{\sqrt{7}}{2} t + \frac{\sqrt{7} c_{1} - 3 c_{2}}{2} e^{- \frac{t}{2}} \sin \frac{\sqrt{7}}{2} t + (c_{3} + \frac{1}{2}) e^{t} + \frac{1}{4} t e^{t} + t + 1 y (t) = c_{1} e^{- \frac{t}{2}} \cos \frac{\sqrt{7}}{2} t + c_{2} e^{- \frac{t}{2}} \sin \frac{\sqrt{7}}{2} t + c_{3} e^{t} + \frac{1}{4} t e^{t} + 1$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.
$x - d^{2} y / d t^{2} = t + 1$
$d x / d t + d y / d t - 2 y = e^{t}$

Step by Step Solution

Step 1: Definition

Step 2: Simplify equation

Step 3: For general solution

Step 4: For particular solution

Step 5: Compute value x

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.x-d2y/dt2=t+1dx/dt+dy/dt-2y=et

Step by Step Solution

Step 1: Definition

Step 2: Simplify equation

Step 3: For general solution

Step 4: For particular solution

Step 5: Compute value x

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In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.
$x - d^{2} y / d t^{2} = t + 1$
$d x / d t + d y / d t - 2 y = e^{t}$