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Beliebt Rechnen >

y^{'''}-9y^{''}+27y^'-27y=8e^{3x}

Lösung

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 8 e^{3 x}

Lösung

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + c_{3} x^{2} e^{3 x} + \frac{4 e ^{3 x} x ^{3}}{3}

Schritte zur Lösung

y^{'''} (x) - 9 y^{''} (x) + 27 y^{'} (x) - 27 y = 8 e^{3 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + c_{3} x^{2} e^{3 x} + \frac{4 e ^{3 x} x ^{3}}{3}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + c_{3} x^{2} e^{3 x} + \frac{4 e ^{3 x} x ^{3}}{3}

Graph

Beliebte Beispiele

(d^2x)/(dt^2)+81x=8sin(9t)

\frac{d ^{2} x}{d t ^{2}} + 81 x = 8 sin (9 t)

y^{^{''}} - y^{^{'}} + 4 = 0

x^{''}-9x=2t^2-cos(t)

x^{^{''}} - 9 x = 2 t^{2} - cos (t)

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

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

3y^'+2y^{''}=-10cos(3.14*t/(0.2))

3 y^{^{'}} + 2 y^{^{''}} = - 10 cos (3.14 \cdot \frac{t}{0.2})