Chapter 8: Q5.2P (page 414)

Solve the following differential equations by the methods discussed above and compare computer solutions.
$y " - 4 y' + 4 y = 0$

Short Answer

Expert verified

The solution is $y = (A x + B) e^{2 x}$

Step by step solution

Given information

A differential equation is given as $y'' - 4 y' + 4 y = 0$ .

Differential equation.

A differential equation of the form $(D - a) (D - b) y = 0$ , $a = b \neq 0$ has general solution

$y = (A x + B) e^{a x}$

Find the solution of given differential equation.

A differential equation is given as $y " - 4 y' + 4 y = 0$ .

Calculation:

Suppose that $D = \frac{d}{d x}$ .

Then

$D y = \frac{d y}{d x} D y = y D^{2} y = \frac{d}{d x} (\frac{d y}{d x}) \frac{d^{2} y}{d x^{2}} = y$

Given differential equation is $y " - 4 y' + 4 y = 0$ .

Above equation becomes,

role="math" localid="1664376798686" $D^{2} y - 4 D y + 4 y = 0 (D^{2} - 4 D + 4) y = 0 (D - 2) (D - 2) y = 0$

$(D - 2) y = 0$ and $(D - 2) y = 0$

The general solution will be given by $y = (A x + B) e^{2 x}$

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Solve the following differential equations by the methods discussed above and compare computer solutions.
$y " - 4 y' + 4 y = 0$

Short Answer

Step by step solution

Given information

Differential equation.

Find the solution of given differential equation.

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Solve the following differential equations by the methods discussed above and compare computer solutions.y"-4y'+4y=0

Short Answer

Step by step solution

Given information

Differential equation.

Find the solution of given differential equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Torque and Rotational Motion

Work Energy and Power

Electricity

Nuclear Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

Solve the following differential equations by the methods discussed above and compare computer solutions.
$y " - 4 y' + 4 y = 0$