What is the d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0 ?

The d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0 is d/(dt((\H(0))(x)))(\H(t((\H(0))(x))))

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d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0

\frac{d}{d t} (H (t)) = 4 - 0.5 H (t), H (0) = 0

\frac{d}{d t ( ( H ( 0 ) ) ( x ) )} (H (t ((H (0)) (x))))

Solution steps

Find

\frac{d}{d t} (H (t)) \circ H (0)

given

\frac{d}{d t} (H (t)) = 4 - 0.5 H (t), H (0) = 0

\frac{d}{d t} (H (t)) \circ H (0) = (\frac{d}{d t} (H (t))) ((H (0)) (x))

(\frac{d}{d t} (H (t))) ((H (0)) (x)) = (\frac{d}{d t ( x )} (H (t (x)))) ((H (0)) (x))

(H (0)) (x) : 0

(\frac{d}{d t ( x )} (H (t (x)))) ((H (0)) (x)) : \frac{d}{d t ( ( H ( 0 ) ) ( x ) )} (H (t ((H (0)) (x))))

= \frac{d}{d t ( ( H ( 0 ) ) ( x ) )} (H (t ((H (0)) (x))))

\frac{d y}{d x} = \frac{10 + 16 x}{x y ^{2}}, y = 4, x = 1

y^{2} + y - x \frac{d y}{d x} = 0

y d x + (x - 6) d y = 0

\frac{y - 1}{5 + x ^{2}} d y = y^{2} d x

y^{^{'}} = 7 x y

What is the d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0 ?
The d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0 is d/(dt((\H(0))(x)))(\H(t((\H(0))(x))))