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Beliebt Rechnen >

y^{''}+4y^'+3y=-19te^{4t}

Lösung

y^{^{''}} + 4 y^{^{'}} + 3 y = - 19 t e^{4 t}

Lösung

y = c_{1} e^{- t} + c_{2} e^{- 3 t} - \frac{19 e ^{4 t} t}{35} + \frac{228}{1225} e^{4 t}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 3 y = - 19 t e^{4 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} - \frac{19 e ^{4 t} t}{35} + \frac{228}{1225} e^{4 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} - \frac{19 e ^{4 t} t}{35} + \frac{228}{1225} e^{4 t}

Graph

Beliebte Beispiele

2 y^{^{''}} - y^{^{'}} = 7

y^{''}+y^'-6y=x^2-x+e^{2x}

y^{^{''}} + y^{^{'}} - 6 y = x^{2} - x + e^{2 x}

y^{''}-10y^'+25y=6e^{-5x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 e^{- 5 x}

y^{''}-5y^'+6y=4,e^{4x}y(0)=0,y^'(0)=1

y^{^{''}} - 5 y^{^{'}} + 6 y = 4, e^{4 x} y (0) = 0, y^{^{'}} (0) = 1

(d^2y)/(dx^2)-5(dy)/(dx)-24y=5+2x

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 24 y = 5 + 2 x