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Beliebt Rechnen >

y^{''}-8y^'+2y=xe^x

Lösung

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

Lösung

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

Graph

Beliebte Beispiele

4y^{''}-4y^'+y=64e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 64 e^{\frac{t}{2}}

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

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

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

x^{''}-4x^'+4x=e^{2t}

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}

y^{''}+4y=4cos(2x)+6cos(x)+8x^2-4x

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x) + 8 x^{2} - 4 x