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Beliebt Rechnen >

y^{''}-y^'-42y=-122t+84t^2

Lösung

y^{^{''}} - y^{^{'}} - 42 y = - 122 t + 84 t^{2}

Lösung

y = c_{1} e^{7 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{1}{6}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 42 y = - 122 t + 84 t^{2}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{1}{6}

y = c_{1} e^{7 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{1}{6}

Graph

Beliebte Beispiele

(d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 36 y = - 4 t + 3

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

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

y^{''}+2y^'=cos(t),y(0)=0

y^{^{''}} + 2 y^{^{'}} = cos (t), y (0) = 0

y^{''}+7y^'=cos(2x)+8e^{-5x}

y^{^{''}} + 7 y^{^{'}} = cos (2 x) + 8 e^{- 5 x}

y^{''}+3y^'-4y=2,y^'(0)=0,y(0)=0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y^{^{'}} (0) = 0, y (0) = 0