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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 6 x + 10 - \frac{2}{25} sin (3 x) + \frac{3}{50} cos (3 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 6 x + 10 - \frac{2}{25} sin (3 x) + \frac{3}{50} cos (3 x)

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 6 x + 10 - \frac{2}{25} sin (3 x) + \frac{3}{50} cos (3 x)

Graph

Beliebte Beispiele

y^{''}+4y=cos(2t),y(0)=0,y^'(0)=0

y^{^{''}} + 4 y = cos (2 t), y (0) = 0, y^{^{'}} (0) = 0

y^{''}+y^'+5y=4e^{-t}cos(2t)

y^{^{''}} + y^{^{'}} + 5 y = 4 e^{- t} cos (2 t)

y^{''}-5y^'+4y=e^{2t}

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{2 t}

y^{''}-6y^'+8y=4e^{4x}

y^{^{''}} - 6 y^{^{'}} + 8 y = 4 e^{4 x}

y^{'''}-y^{''}=6

y^{^{'''}} - y^{^{''}} = 6