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Beliebt Rechnen >

y^{''}-2y^'+y=12x^3e^x

Lösung

y^{^{''}} - 2 y^{^{'}} + y = 12 x^{3} e^{x}

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{3 e ^{x} x ^{5}}{5}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + y = 12 x^{3} e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{3 e ^{x} x ^{5}}{5}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{3 e ^{x} x ^{5}}{5}

Graph

Beliebte Beispiele

2y^{''}-2y^'-4y=2e^{2t}

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{2 t}

y^{'''}+6y^{''}+11y^'+6y=3+3x

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 + 3 x

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

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

y^{''}+y=6sin(2x)

y^{^{''}} + y = 6 sin (2 x)

(D^2-3D+2)y=cos(3x)

(D^{2} - 3 D + 2) y = cos (3 x)