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Beliebt Rechnen >

y^{'''}-12y^{''}+256y=e^{8x}

Lösung

y^{^{'''}} - 12 y^{^{''}} + 256 y = e^{8 x}

Lösung

y = c_{1} e^{- 4 x} + c_{2} e^{8 x} + c_{3} x e^{8 x} + \frac{e ^{8 x} x ^{2}}{24}

Schritte zur Lösung

y^{'''} (x) - 12 y^{''} (x) + 256 y = e^{8 x}

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{8 x} + c_{3} x e^{8 x} + \frac{e ^{8 x} x ^{2}}{24}

y = c_{1} e^{- 4 x} + c_{2} e^{8 x} + c_{3} x e^{8 x} + \frac{e ^{8 x} x ^{2}}{24}

Graph

Beliebte Beispiele

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

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

1/2 x^{''}+1/2 x^'+6x=10cos(3t)

\frac{1}{2} x^{^{''}} + \frac{1}{2} x^{^{'}} + 6 x = 10 cos (3 t)

y^{''}-y^'=4cos(2x)

y^{^{''}} - y^{^{'}} = 4 cos (2 x)

8y^{''}+4y^'+5y=1,y(0)=1

8 y^{^{''}} + 4 y^{^{'}} + 5 y = 1, y (0) = 1

y^{'''}-4y^'=cot(2x)

y^{^{'''}} - 4 y^{^{'}} = cot (2 x)