(dy)/(dt)= 1/5 t

解答

\frac{d y}{d t} = \frac{1}{5} t

y = \frac{t ^{2}}{10} + c_{1}

求解步骤

\frac{d y}{d t} = \frac{1}{5} t

替代

\frac{d y}{d t}

与

y^{'} (t)

y^{^{'}} (t) = \frac{1}{5} t

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

y = \int \frac{1}{5} t d t

\int \frac{1}{5} t d t = \frac{t ^{2}}{10} + c_{1}

y = \frac{t ^{2}}{10} + c_{1}

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 12, y^{^{'}} (0) = b

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