25y^{''}+20y^'+4y=4x^2-3x+2

Lösung

25 y^{^{''}} + 20 y^{^{'}} + 4 y = 4 x^{2} - 3 x + 2

y = c_{1} e^{- \frac{2 x}{5}} + c_{2} e^{- \frac{2 x}{5}} x + x^{2} - \frac{43 x}{4} + \frac{167}{4}

Schritte zur Lösung

25 y^{''} (x) + 20 y^{'} (x) + 4 y = 4 x^{2} - 3 x + 2

Solve linear ODE:

y = c_{1} e^{- \frac{2 x}{5}} + c_{2} e^{- \frac{2 x}{5}} x + x^{2} - \frac{43 x}{4} + \frac{167}{4}

y = c_{1} e^{- \frac{2 x}{5}} + c_{2} e^{- \frac{2 x}{5}} x + x^{2} - \frac{43 x}{4} + \frac{167}{4}

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

y^{^{''}} + 6 y^{^{'}} + 5 y = 3 e^{- x}

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 x + 1, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 9 y^{^{'}} + 5 y = x e^{x}