y^{''}-y^'+1/4 y=9+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 9 + e^{\frac{x}{2}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + \frac{1}{4} y = 9 + e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y^{^{''}} + 4 y = 9 sec (2 x)

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

(D^{2} + 1) y = csc (x)

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

y^{^{''}} - 4 y = e^{x}