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Beliebt Rechnen >

y^{''}-4y^'=xe^{4x}

Lösung

y^{^{''}} - 4 y^{^{'}} = x e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

Graph

Beliebte Beispiele

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

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = e^{\frac{x}{2}} 1 - x^{2}

y^{'''}+y^'=sec(t)

y^{^{'''}} + y^{^{'}} = sec (t)

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

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

y^{'''}+y^'=tan(t)

y^{^{'''}} + y^{^{'}} = tan (t)