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人気のある微分積分 >

25y^{''}-40y^'+16y=0,y(0)=4,y^'(0)=-3

解

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = - 3

解

y = 4 e^{\frac{4 t}{5}} - \frac{31 e ^{\frac{4 t}{5}} t}{5}

解答ステップ

25 y^{''} (t) - 40 y^{'} (t) + 16 y = 0

線形 ODE を解く:

y = 4 e^{\frac{4 t}{5}} - \frac{31 e ^{\frac{4 t}{5}} t}{5}

y = 4 e^{\frac{4 t}{5}} - \frac{31 e ^{\frac{4 t}{5}} t}{5}

グラフ

人気の例

y^{''}-16y=0,y(0)=3,y^'(0)=5

y^{^{''}} - 16 y = 0, y (0) = 3, y^{^{'}} (0) = 5

(d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0

\frac{d ^{4} y}{d x ^{4}} - \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

(d^2y)/(dx^2)=0.15y,y(0)=240,y(10)=150

\frac{d ^{2} y}{d x ^{2}} = 0.15 y, y (0) = 240, y (10) = 150

y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = - 16

y = 10 y^{^{''}}