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Beliebt Rechnen >

y^{'''}-3y^{''}+3y^'-y-e^x=0

Lösung

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y - e^{x} = 0

Lösung

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

Schritte zur Lösung

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y - e^{x} = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

x^{''}+x^'+x=1,x^'(0)=0

x^{^{''}} + x^{^{'}} + x = 1, x^{^{'}} (0) = 0

y^{''}-8y^'+4y=8e^{2x}

y^{^{''}} - 8 y^{^{'}} + 4 y = 8 e^{2 x}

y^{''}+2y^'+y=t,y(0)=t,y^'(0)=2

y^{^{''}} + 2 y^{^{'}} + y = t, y (0) = t, y^{^{'}} (0) = 2

y^{''}-2y^'+y=3e^{-x}

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{- x}

y^{''''}+9y^{''}=sec^2(3t)

y^{^{''''}} + 9 y^{^{''}} = sec^{2} (3 t)