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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{2}}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{2}}{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{2}}{2}

Graph

Beliebte Beispiele

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

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

y^{''}-a^2y=-2sin(pi*x)-4sin(3*pi*x)

y^{^{''}} - a^{2} y = - 2 sin (π \cdot x) - 4 sin (3 \cdot π \cdot x)

(d - 2) y = e^{2} x

y^{''}+7/2 y^'+3/2 y=2e^{-3x}

y^{^{''}} + \frac{7}{2} y^{^{'}} + \frac{3}{2} y = 2 e^{- 3 x}

y^{''}+4^2y=cos(2t)

y^{^{''}} + 4^{2} y = cos (2 t)