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Calculus Level 3

\[ \frac{\textrm{d}^2y}{\textrm{d}x^2}+\frac{\textrm{d}y}{\textrm{d}x}=0; \: \: \: y(i \pi)=0 \:\:\: \textrm{and} \:\:\: y \; '( \ln 2)=1 \]

The solution to the above second-order differential equation can be determined as \(y= f(x) \).

It is known that the function evaluated at \( \ln 4 \) can be written as

\[ f( \ln 4)= -\frac{a}{b} \]

Determine the value of \( a+b \)

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