I’1 point ; Find the function * I of & which is the solution of 36%’ – 4* = 0 with initial conditions* *1 1 0 ) = 1 . *’ 101 – 0. .5 exp /sort / 4 / 36;t ) + .5 expl – sart /4 / 36;t) Find the function *2 of I which is the solution of 36*" – AY = 0

I’1 point ; Find the function * I of & which is the solution of
36%’ – 4* = 0
with initial conditions* *1 1 0 ) = 1 . *’ 101 – 0.
.5 exp /sort / 4 / 36;t ) + .5 expl – sart /4 / 36;t)
Find the function *2 of I which is the solution of
36*" – AY = 0
with initial conditions 12 1 0 ) = 0, W`[oj = 1 .
1/ 2 =| (1 /2 sort /4 / 35 )jexp ( $art / 4 / 35)+) – (1/ 1259/1/4/ 35 )jexp (- sort| 4 / 3614 )
Find the Wronskian
H` ( T ) = W` ( `’ 1 , 82)`
( Hint : write !’ I and My in terms of hyperbolic sine and cosine and use properties of the hyperbolic
functions ) .
W ( 1 )
Remark: You should find that W is not zero and so *’ , and My form a fundamental set of solutions of
36* " – 4Y = 0 .

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