Mathematics, 04.08.2019 05:00 jameslinimk
Determine a, b, and c so that y=acosh(cx)+bsinh(cx)satisfies the conditions y′′−4y=0,y(0)=3,y′(0)=3. take c> 0.
Answers: 1
.
:
.
:
are possible choices, which makes 
, respectively.
, we can eliminate the factor of 
to get
, we have equality, but this goes against our assumption that 
. Note that 
for all 
, which means 
is a monotonically increasing function, and is bounded between -1 and 1. On the other hand, 
is a monotonically decreasing function that is unbounded. From this you can gather that the two functions never intersect for 
(since 
is always positive), which means 
. So, in fact, the equation above has no solution for 
.
, 
, and 
.
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Determine a, b, and c so that y=acosh(cx)+bsinh(cx)satisfies the conditions y′′−4y=0,y(0)=3,y′(0)=3....
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