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人気のある微分積分 >

(dv)/(dt)=k\sqrt[3]{v^2},v(0)=27

解

\frac{d v}{d t} = k 3 v^{2}, v (0) = 27

解

v = \frac{k ^{3} t ^{3}}{27} + k^{2} t^{2} + 9 k t + 27

解答ステップ

\frac{d v}{d t} = k 3 v^{2}

分離可能 ODE を解く:

v = \frac{k ^{3} t ^{3}}{27} + k^{2} t^{2} + 9 k t + 27

v = \frac{k ^{3} t ^{3}}{27} + k^{2} t^{2} + 9 k t + 27

グラフ

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