MHB Find the unique solution to the IVP

[shamieh]

Find the unique solution to the IVP

$t^3y'' + e^ty' + t^4y = 0$ $y(1) = 0$ , $y'(1) = 0$

Should I start out by dividing through by $t^4$

to get

$\frac{1}{t} y" + \frac{e^t}{t^4}y' + y = 0$

 

[MarkFL]

I think in this case, you should look for a trivial solution to the given ODE. :D

 

[shamieh]

what do you mean? should I plug y(1) = 0

 

[MarkFL]

Consider the function:

$$y(t)=0$$

Does it satisfy all of the given requirements?

 

[shamieh]

Yes?

 

[shamieh]

Consider the function:

$$y(t)=0$$

Does it satisfy all of the given requirements?

Oh wait.. I need to test this using the exact solution method don't i?

(testing whether it is exact or not)

 

[MarkFL]

Oh wait.. I need to test this using the exact solution method don't i?

(testing whether it is exact or not)

That's for first order equations...to be honest, I would not know offhand how to find the general solution to the ODE associated with the IVP here, but I simply noticed that the trivial solution $y(t)=0$ satisfies the IVP. :D