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## Main Question or Discussion Point

I would like to solve the following differential equation, it seems easy but only given one initial value.

y''(x) = ln(ln(x))

y(5) = 0

Solve for y(10)

I know it can be directly integrated but cannot be expressed in terms of elementary functions.

Most numerical method involves expressing the ODE in terms of first order ODE, but it need to have to initial value of y and also y'.

Is it even possible to solve this, given only y(5) = 0?

y''(x) = ln(ln(x))

y(5) = 0

Solve for y(10)

I know it can be directly integrated but cannot be expressed in terms of elementary functions.

Most numerical method involves expressing the ODE in terms of first order ODE, but it need to have to initial value of y and also y'.

Is it even possible to solve this, given only y(5) = 0?