Could you please write clearly! Thank you 1Verify that y = C1x + c2vx+is the general solution of the6x1following nonhomogeneous 2x²y/" – xy/ + y =

Name: Could you please write clearly! Thank you 1Verify that y = C1x + c2vx+
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Description: Could you please write clearly! Thank you 1Verify that y = C1x + c2vx+is the general solution of the6x1following nonhomogeneous 2x²y/" – xy/ + y =

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Could you please write clearly! Thank you

1
Verify that y = C1x + c2vx+
is the general solution of the
6x
1
following nonhomogeneous 2x²y/" – xy/ + y =

Expert Solution

Step 1

Derivative of $x^{n}$ :

Derivative of an exponential function that is, $x^{n}$ is given by the formula,

$\frac{d}{d x} (x^{n}) = n x^{n - 1}$

Given:

It is given that, the non-homogeneous differential equation is $2 x^{2} y'' - x y' + y = \frac{1}{x}$ .

To verify:

We have to verify that, $y = c_{1} x + c_{2} \sqrt{x} + \frac{1}{6 x}$ is the solution of the given differential equation.

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