Help finding general solution for 2nd order linear DE

[Jende]

Homework Statement

Find the general solution for the DE: t²y''-2y=0

Homework Equations

These were given for other parts of the problem so I'm not sure if they're relevant.
y₁(t)=t², y₂(t)=t^-1, y(1)=-2, y'(1)=-7

The Attempt at a Solution

The t² at the front was really stumping me and I'm not sure where to begin.

Thanks in advance for any help.

 

[LCKurtz]

Homework Statement

Find the general solution for the DE: t²y''-2y=0

Homework Equations

These were given for other parts of the problem so I'm not sure if they're relevant.
y₁(t)=t², y₂(t)=t^-1, y(1)=-2, y'(1)=-7

The Attempt at a Solution

The t² at the front was really stumping me and I'm not sure where to begin.

Thanks in advance for any help.

The earlier parts are relevant. What are $y_1(t)$ and $y_2(t)$? That is, what do they have to do with this problem? Once you answer that, what do you know about solutions of linear equations?

 

[Jende]

The earlier parts are relevant. What are $y_1(t)$ and $y_2(t)$? That is, what do they have to do with this problem? Once you answer that, what do you know about solutions of linear equations?

So it should come out to be: y(x)=C₁t²+C₂t^-1

 

[LCKurtz]

So it should come out to be: y(x)=C₁t²+C₂t^-1

So what should come out that? And does it?

 

[Mark44]

So it should come out to be: y(x)=C₁t²+C₂t^-1

The independent variable is t, not x, so the above should be y(t)=C₁t²+C₂t^-1