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Beliebt Rechnen >

y^{'''}-6y^{''}+12y^'-8y=t^3e^{2t}+1

Lösung

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t} + 1

Lösung

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} t^{2} e^{2 t} + \frac{e ^{2 t} t ^{6} - 15}{120}

Schritte zur Lösung

y^{'''} (t) - 6 y^{''} (t) + 12 y^{'} (t) - 8 y = t^{3} e^{2 t} + 1

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} t^{2} e^{2 t} + \frac{e ^{2 t} t ^{6} - 15}{120}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} t^{2} e^{2 t} + \frac{e ^{2 t} t ^{6} - 15}{120}

Graph

Beliebte Beispiele

y^{''}+4y=e^{3x}+xsin(2x)

y^{^{''}} + 4 y = e^{3 x} + x sin (2 x)

y^{''}+3y^'+2y= 1/((1+e^x))

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 1 + e ^{x} )}

y^{'''}-9y^{''}+108y=e^{6x}

y^{^{'''}} - 9 y^{^{''}} + 108 y = e^{6 x}

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

(d^2y)/(dt^2)-y=e^t

\frac{d ^{2} y}{d t ^{2}} - y = e^{t}