Consider given BVP y''-4y=0, y(0)=0 , y(1)=0
Consider y''-4y=0
Therefore auxiliary equation is
m2-4=0
I. e m2=4
I. e m=2 or m=-2,
Therfore general solution is
y=C1e-2x+C2e2x ........ ......... (1)
Given that y(0)=0 and y(1)=0
Therefore equation (1) becomes
y(0)=C1e0+C2e0
0=C1+C2 ............... (2)
And
y(1)=C1e-2+C2e2
0= C1e-2+C2e2............(3)
Now solving equation (2),and (3)
We get a C1=C2=0 this implies
y=0 is only solution of given BVP
Note that given initial conditions are wrong. I think
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