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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- \frac{x}{2}} x + \frac{e ^{- \frac{x}{2}} x ^{2}}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- \frac{x}{2}} x + \frac{e ^{- \frac{x}{2}} x ^{2}}{8}

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- \frac{x}{2}} x + \frac{e ^{- \frac{x}{2}} x ^{2}}{8}

Graph

Beliebte Beispiele

y^{''''}+y^{''}=x^2+x

y^{^{''''}} + y^{^{''}} = x^{2} + x

y^{''}-y^'-6y=e^{3x}+30

y^{^{''}} - y^{^{'}} - 6 y = e^{3 x} + 30

y^{'''}+y^{''}=e^x

y^{^{'''}} + y^{^{''}} = e^{x}

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

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

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

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