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Beliebt Rechnen >

y^{''}-8y^'+16y=1-x+e^{4x}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = 1 - x + e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} x e^{4 x} - \frac{x}{16} + \frac{1}{32} + \frac{e ^{4 x} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = 1 - x + e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} - \frac{x}{16} + \frac{1}{32} + \frac{e ^{4 x} x ^{2}}{2}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} - \frac{x}{16} + \frac{1}{32} + \frac{e ^{4 x} x ^{2}}{2}

Graph

Beliebte Beispiele

y^{''}-y^'-6y=csc(x)

y^{^{''}} - y^{^{'}} - 6 y = csc (x)

y^{'''}-2y^{''}-5y^'+6y=e^{-2x}

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = e^{- 2 x}

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

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

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

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

y^{''}-2y^'+10y=15x^2-x+1

y^{^{''}} - 2 y^{^{'}} + 10 y = 15 x^{2} - x + 1