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人気のある微分積分 >

y^{''}-y^'+400y=20sin(20t)

解

y^{^{''}} - y^{^{'}} + 400 y = 20 sin (20 t)

解

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

解答ステップ

y^{''} (t) - y^{'} (t) + 400 y = 20 sin (20 t)

線形 ODE を解く:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

グラフ

人気の例

4y^{''}-y=xe^{x/2},y(0)=1,y^'(0)=0

4 y^{^{''}} - y = x e^{\frac{x}{2}}, y (0) = 1, y^{^{'}} (0) = 0

y^{''}+9y=g(t),y(0)=1,y^'(0)=0

y^{^{''}} + 9 y = g (t), y (0) = 1, y^{^{'}} (0) = 0

y^{''}-4y^'-12y=3x^2-5x+4-3e^{-3x}

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 x^{2} - 5 x + 4 - 3 e^{- 3 x}

y^{^{''}} + y = 2 e^{x}

y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6

y^{^{''}} - y^{^{'}} - 6 y = 15 e^{3 t}, y (0) = 2, y^{^{'}} (0) = - 6