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Beliebt Rechnen >

y^{''}+3y^'+2y=e^x,y(0)=0,y^'(0)=3

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{x}, y (0) = 0, y^{^{'}} (0) = 3

Lösung

y = (\frac{8}{3} - \frac{1}{6}) e^{- x} - \frac{8}{3} e^{- 2 x} + \frac{1}{6} e^{x}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 2 y = e^{x}

Solve linear ODE:

y = (\frac{8}{3} - \frac{1}{6}) e^{- x} - \frac{8}{3} e^{- 2 x} + \frac{1}{6} e^{x}

y = (\frac{8}{3} - \frac{1}{6}) e^{- x} - \frac{8}{3} e^{- 2 x} + \frac{1}{6} e^{x}

Graph

Beliebte Beispiele

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

y^{^{''}} - y^{^{'}} + \frac{y}{4} = 3 + e^{\frac{x}{2}}

y^{''}+10y^'+16y=40cos(4x)

y^{^{''}} + 10 y^{^{'}} + 16 y = 40 cos (4 x)

y^{''}-8y^'+6y=3x^2-8

y^{^{''}} - 8 y^{^{'}} + 6 y = 3 x^{2} - 8

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

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

y^{'''}+y^{''}-2y=-e^{3x}(9+67x+17x^2)

y^{^{'''}} + y^{^{''}} - 2 y = - e^{3 x} (9 + 67 x + 17 x^{2})