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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

(d^2-6d+9)y=2e^3x

(d^{2} - 6 d + 9) y = 2 e^{3} x

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

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

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

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

(d^2-1)*y=x*sin(x)+x^2*e^x

(d^{2} - 1) \cdot y = x \cdot sin (x) + x^{2} \cdot e^{x}