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Beliebt Rechnen >

y^{''''}+y^{'''}=1-x^2e^{-x}

Lösung

y^{^{''''}} + y^{^{'''}} = 1 - x^{2} e^{- x}

Lösung

y = c_{1} e^{- x} + c_{2} + c_{3} x + c_{4} x^{2} + \frac{2 x ^{3} + e ^{x} x ^{3} + 18 x ^{2} - 3 e ^{x} x ^{2} + 72 x + 6 e ^{x} x + 120}{6 e ^{x}} - 1

Schritte zur Lösung

y^{(4)} (x) + y^{'''} (x) = 1 - x^{2} e^{- x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + c_{4} x^{2} + \frac{2 x ^{3} + e ^{x} x ^{3} + 18 x ^{2} - 3 e ^{x} x ^{2} + 72 x + 6 e ^{x} x + 120}{6 e ^{x}} - 1

y = c_{1} e^{- x} + c_{2} + c_{3} x + c_{4} x^{2} + \frac{2 x ^{3} + e ^{x} x ^{3} + 18 x ^{2} - 3 e ^{x} x ^{2} + 72 x + 6 e ^{x} x + 120}{6 e ^{x}} - 1

Graph

Beliebte Beispiele

y^{''}-5y^'+6y=8xe^x

y^{^{''}} - 5 y^{^{'}} + 6 y = 8 x e^{x}

y^{''}+3y^'=1-e^{-3x}

y^{^{''}} + 3 y^{^{'}} = 1 - e^{- 3 x}

y^{''}+16y=6x,y(0)=1,y^'(0)=4

y^{^{''}} + 16 y = 6 x, y (0) = 1, y^{^{'}} (0) = 4

y^{''}-2y^'-3y=-11te^{-t}

y^{^{''}} - 2 y^{^{'}} - 3 y = - 11 t e^{- t}

y^{''}-4y^'+8y=x^3-x

y^{^{''}} - 4 y^{^{'}} + 8 y = x^{3} - x