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Beliebt Rechnen >

y^{''}-4y^'+4y=-7x+4x^2

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = - 7 x + 4 x^{2}

Lösung

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

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = - 7 x + 4 x^{2}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

0.5y^{''}+y^'+4y=10sin(2x)

0.5 y^{^{''}} + y^{^{'}} + 4 y = 10 sin (2 x)

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

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

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

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

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

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

x^{^{''}} + a x = b