solve the given differential equation.

Chapter 4, Problem 8E

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QUESTION:

In Problems 1–18 solve the given differential equation.

\(x^{2} y^{\prime \prime}+3 x y^{\prime}-4 y=0\)

Text Transcription:

x^2 y^prime prime+3 x y^prime-4 y=0

Questions & Answers

QUESTION:

In Problems 1–18 solve the given differential equation.

\(x^{2} y^{\prime \prime}+3 x y^{\prime}-4 y=0\)

Text Transcription:

x^2 y^prime prime+3 x y^prime-4 y=0

ANSWER:

Step 1 of 3

A second order Euler homogeneous ODE has the form of

For an equation , assume a solution of the form  

Rewrite the equation with

Simplify

Solve

For two real roots , the general solution takes the form :

Therefore,

 

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