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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

Graph

Beliebte Beispiele

y^{''}-12y^'+32y=4cos(3t)

y^{^{''}} - 12 y^{^{'}} + 32 y = 4 cos (3 t)

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

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

y^{''}-4y^'+20y=2sin(3t)

y^{^{''}} - 4 y^{^{'}} + 20 y = 2 sin (3 t)

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

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

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

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 3 y = e^{2 x}