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人気のある微分積分 >

4(d^2x)/(dt^2)+c(dx)/(dt)+k(x)=0

解

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

解

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

解答ステップ

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

線形 ODE を解く:

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

グラフ

人気の例

y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=18

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 18

16y^{''}-8y+145y=0,y(0)=-2,y^'(0)=1

16 y^{^{''}} - 8 y + 145 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

y^{'''}-3y^{''}-13y^'+15y=0

y^{^{'''}} - 3 y^{^{''}} - 13 y^{^{'}} + 15 y = 0

27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0

27 y^{^{''}} + (15 - 95) y^{^{'}} - 55 y = 0

324y^{''}-612y^'+289y=0,y(0)=8,y^'(0)=5

324 y^{^{''}} - 612 y^{^{'}} + 289 y = 0, y (0) = 8, y^{^{'}} (0) = 5