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Beliebt Rechnen >

25y^{''}-y=xe^{1/5 x}

Lösung

25 y^{^{''}} - y = x e^{\frac{1}{5} x}

Lösung

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{- \frac{x}{5}} + \frac{e ^{\frac{x}{5}} x ^{2}}{20} - \frac{1}{8} e^{- \frac{x}{5}} (2 e^{\frac{2 x}{5}} x - 5 e^{\frac{2 x}{5}})

Schritte zur Lösung

25 y^{''} (x) - y = x e^{\frac{1}{5} x}

Solve linear ODE:

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{- \frac{x}{5}} + \frac{e ^{\frac{x}{5}} x ^{2}}{20} - \frac{1}{8} e^{- \frac{x}{5}} (2 e^{\frac{2 x}{5}} x - 5 e^{\frac{2 x}{5}})

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{- \frac{x}{5}} + \frac{e ^{\frac{x}{5}} x ^{2}}{20} - \frac{1}{8} e^{- \frac{x}{5}} (2 e^{\frac{2 x}{5}} x - 5 e^{\frac{2 x}{5}})

Graph

Beliebte Beispiele

3x^{''}+10x=2sin(3t)

3 x^{^{''}} + 10 x = 2 sin (3 t)

y^{''}-y^'-6y=(10x+7)e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = (10 x + 7) e^{3 x}

y^{''}-3y^'+2y=e^{4t}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{4 t}

y^{''}+4y^'+5y=e^{-x}+15x

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- x} + 15 x

x^{''}+9.8x=cos(2t)

x^{^{''}} + 9.8 x = cos (2 t)