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Beliebt Rechnen >

2y^{''}+y^'+4y=x+1

Lösung

2 y^{^{''}} + y^{^{'}} + 4 y = x + 1

Lösung

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{31 x}{4}) + c_{2} sin (\frac{31 x}{4})) + \frac{x}{4} + \frac{3}{16}

Schritte zur Lösung

2 y^{''} (x) + y^{'} (x) + 4 y = x + 1

Solve linear ODE:

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{31 x}{4}) + c_{2} sin (\frac{31 x}{4})) + \frac{x}{4} + \frac{3}{16}

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{31 x}{4}) + c_{2} sin (\frac{31 x}{4})) + \frac{x}{4} + \frac{3}{16}

Graph

Beliebte Beispiele

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

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

y^{''}-y^'-6y=5-6^x,y(0)=2,y^'(0)=4

y^{^{''}} - y^{^{'}} - 6 y = 5 - 6^{x}, y (0) = 2, y^{^{'}} (0) = 4

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

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

x^{''}-6x+9x=126t^2e^{3t}

x^{^{''}} - 6 x + 9 x = 126 t^{2} e^{3 t}

y^{''}+9*y^'=5t

y^{^{''}} + 9 \cdot y^{^{'}} = 5 t