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Beliebt Rechnen >

y^{'''}-18y^{''}+864y=e^{12x}

Lösung

y^{^{'''}} - 18 y^{^{''}} + 864 y = e^{12 x}

Lösung

y = c_{1} e^{- 6 x} + c_{2} e^{12 x} + c_{3} x e^{12 x} + \frac{e ^{12 x} x ^{2}}{36}

Schritte zur Lösung

y^{'''} (x) - 18 y^{''} (x) + 864 y = e^{12 x}

Solve linear ODE:

y = c_{1} e^{- 6 x} + c_{2} e^{12 x} + c_{3} x e^{12 x} + \frac{e ^{12 x} x ^{2}}{36}

y = c_{1} e^{- 6 x} + c_{2} e^{12 x} + c_{3} x e^{12 x} + \frac{e ^{12 x} x ^{2}}{36}

Graph

Beliebte Beispiele

(D^{3} - D) y = x

y^{''}+y^'=16e^{3x}

y^{^{''}} + y^{^{'}} = 16 e^{3 x}

(d^2y)/(dx^2)+3(dy)/(dx)+2y= 1/(1+e^x)

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = \frac{1}{1 + e ^{x}}

y^{''}-y^'+169y=13sin(13t)

y^{^{''}} - y^{^{'}} + 169 y = 13 sin (13 t)

y^{''}+4y=sin(t),y(0)=0,y^'(0)=0

y^{^{''}} + 4 y = sin (t), y (0) = 0, y^{^{'}} (0) = 0