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Determine the largest interval in which the given initial value problem is certain to have a...

Determine the largest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution.

sin(t)d^2x/dt^2+cos(t)dxdt+sin(t)x=tan(t) ,x(1)=20,x′(1)=5

Interval:

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