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人気のある微分積分 >

y^{''}-2y^'+y=(9e^t)/(1+t^2)

解

y^{^{''}} - 2 y^{^{'}} + y = \frac{9 e ^{t}}{1 + t ^{2}}

解

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{9}{2} e^{t} ln (1 + t^{2}) + 9 e^{t} t arctan (t)

解答ステップ

y^{''} (t) - 2 y^{'} (t) + y = \frac{9 e ^{t}}{1 + t ^{2}}

線形 ODE を解く:

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{9}{2} e^{t} ln (1 + t^{2}) + 9 e^{t} t arctan (t)

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{9}{2} e^{t} ln (1 + t^{2}) + 9 e^{t} t arctan (t)

グラフ

人気の例

(d^2y)/(dx^2)-pi^2y=xcos(x)

\frac{d ^{2} y}{d x ^{2}} - π^{2} y = x cos (x)

y^{'''}-4y^{''}+5y^'-2y=-6ex+10cos(x)

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = - 6 e x + 10 cos (x)

(d^3y)/(dx^3)-(d^2y)/(dx^2)=e^x

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = e^{x}

x^{''}-18x^'+81x=te^{9t}

x^{^{''}} - 18 x^{^{'}} + 81 x = t e^{9 t}

x^{''}-4x^'-5x=2+e^{-t}

x^{^{''}} - 4 x^{^{'}} - 5 x = 2 + e^{- t}