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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

Graph

Beliebte Beispiele

y^{''}+3y^'+2y=6e^x

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{x}

y^{''}-10y^'+25y=(x+1)e^x

y^{^{''}} - 10 y^{^{'}} + 25 y = (x + 1) e^{x}

y^{'''}-5y^{''}=4x^2-3x+6e^{5x}

y^{^{'''}} - 5 y^{^{''}} = 4 x^{2} - 3 x + 6 e^{5 x}

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

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

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

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