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Beliebt Rechnen >

y^{''}-5y^'+6y=x^2-3x+1

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2} - 3 x + 1

Lösung

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} - \frac{2 x}{9} - \frac{2}{27}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 6 y = x^{2} - 3 x + 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} - \frac{2 x}{9} - \frac{2}{27}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} - \frac{2 x}{9} - \frac{2}{27}

Graph

Beliebte Beispiele

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

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

y^{''}+2y^'+2y=e^{-1}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- 1}

2y^{''}+3y^'-2y=-8x-13,y(0)=0,y^'(0)=0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = - 8 x - 13, y (0) = 0, y^{^{'}} (0) = 0

2x^{''}-x^'+4x=cos(3t)

2 x^{^{''}} - x^{^{'}} + 4 x = cos (3 t)

y^{''}+9y=5sin(x)

y^{^{''}} + 9 y = 5 sin (x)