determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution
t(t-4)y'' +3ty'+4y = 2; y(3)=0, y'(3) =-1
Please, walk me through.

Question

determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution
t(t-4)y'' +3ty'+4y = 2; y(3)=0, y'(3) =-1
Please, walk me through.

loser66 · Answer

give me strategy, please

amistre64 · Answer

the most obvious is that t(t-4) cannot be zero

loser66 · Answer

the net is so bad here. so if you see I "disappear", I apology.

loser66 · Answer

yes, so?

amistre64 · Answer

we see that we want t=3 in the interval,  and without solving we know that t=0 and t=4 are bad areas

amistre64 · Answer

so without solving, the best guess would be:  0 < t < 4

loser66 · Answer

thanks for a perfect analysis. it's the answer from book. Thanks a tooon

amistre64 · Answer

youre welcome

loser66 · Answer

how about the "unique twice-differentiable solution"? what does it mean? @amistre64

amistre64 · Answer

in order to get to y'' you need to be able to differentiate it 2 times right?

amistre64 · Answer

its just extra verbiage to make the question more rigorous

loser66 · Answer

really? ok, wonder how and why they have to do that. life is not hard enough? hehehe

amistre64 · Answer

:)  the text wil most likely drop that shortly stating that all examples/questions assume the rigor

loser66 · Answer

thanks again.