-b.1.3.12 .... is a solution of the DE

[karush]

Spoiler: source

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#12 hope I rewrote the problem ok

Verify that $y_2(t)=t^{-2}\ln t\quad y_1(t)=t^{-2}$ is a solution of $t^2y''+5ty'+4y=0$
think the first steop is to compose a charactistic equation using r

 

[skeeter]

$y_1(t) = t^{-2} \implies y'_1(t) = -2t^{-3} \implies y''_1(t) = 6t^{-4}$

$t^2 \cdot 6t^{-4} + 5t \cdot(-2t^{-3}) + 4 \cdot t^{-2} = 6t^{-2} - 10t^{-2} + 4t^{-2} = 0$

verified

 

[karush]

so that is how it is done...
the examples were pretty mind numbing compared

I really think MHB should write textbooks...

 

[topsquark]

so that is how it is done...
the examples were pretty mind numbing compared

I really think MHB should write textbooks...

You are merely supposed to verify the solutions. So just plug them in. Solving the equation, on the other hand, can be a bit mind numbing until you get used to it.

-Dan