# Euler Differential Equation

• dave4000

## Homework Statement

Solve the euler differential equation

$$\x^{2}y^{''}+3xy'-3y=0$$
$$\int_X f = \lim\int_X f_n < \infty$$
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?

Last edited:
Latex isn't working on this post so here it is without Latex:

## Homework Statement

Solve the euler differential equation

x^{2}y''+3xy'-3y=0

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

## The Attempt at a Solution

y(x)=cx^{m}
y'(x)=cmx^{m-1}
y''(x)=cm(m-1)x^{m-2}

m(m-1)+3m-3=0
m^2+2m-3=0
(m-1)(m+3)=0
m=3 or m=-1

Is this the solution or can c be found?

Last edited:
Latex maybe out due to technical problems.

Is one sure of the function before the y' term - 3x^{2}?