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## Homework Statement

Solve the euler differential equation

[tex]\x^{2}y^{''}+3xy'-3y=0[/tex]

[tex]

\int_X f = \lim\int_X f_n < \infty

[/tex]

by making the ansatz [tex]y(x)=cx^{m}[tex], where c and m are constants.

## The Attempt at a Solution

[tex]y(x)0=c^{m}[tex]

[tex]y^{'}(x)=cm^{m-1}[tex]

[tex]y^{''}(x)=cm(m-1)^{m-2}[tex]

[tex]m(m-1)+3m-3=0[tex]

[tex]m^2+2m-3=0[tex]

[tex](m-1)(m+3)=0[tex]

[tex]m=-3 or m=1[tex]

Is this the solution or can c be found?

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