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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y=e^{2x},y(0)=0

y^{^{''}} + y = e^{2 x}, y (0) = 0

y^{''}-2y^'-3y=xe^{-x}

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

x^{^{''}} + x = 2 e^{t}

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

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

y^{^{''}} = x - y