WebSep 4, 2015 · d d t ( ( x ′ ( t)) 2 + 16 x ( t) 2) = 0. Integrating from 0 to t, we find that. ( x ′ ( t)) 2 + 16 x ( t) 2 = ( x ′ ( 0)) 2 + 16 x ( 0) 2 = 100. Thus, x ′ ( t) = ± 100 − 16 x ( t) 2, where the plus has to be taken, since x ′ ( 0) = 10. This is a separable differential equation, x ′ ( t) 100 − 16 x ( t) 2 = 1. Integrating from ...

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