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

Lösung

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

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} cos (\frac{x}{2}) \cdot \int - 4 e^{\frac{x}{2}} x sin (\frac{x}{2}) d x + e^{- \frac{x}{2}} sin (\frac{x}{2}) \cdot \int 4 e^{\frac{x}{2}} x cos (\frac{x}{2}) d x

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} cos (\frac{x}{2}) \cdot \int - 4 e^{\frac{x}{2}} x sin (\frac{x}{2}) d x + e^{- \frac{x}{2}} sin (\frac{x}{2}) \cdot \int 4 e^{\frac{x}{2}} x cos (\frac{x}{2}) d x

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} cos (\frac{x}{2}) \cdot \int - 4 e^{\frac{x}{2}} x sin (\frac{x}{2}) d x + e^{- \frac{x}{2}} sin (\frac{x}{2}) \cdot \int 4 e^{\frac{x}{2}} x cos (\frac{x}{2}) d x

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{- x} cos (2 x)

y^{^{''}} + 5 y^{^{'}} - 6 y = x e^{- 5 x}

y^{^{''}} + 7 y^{^{'}} + 12 y = t^{2} e^{- 3 t}

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