y^{''}-y^'+14y=4+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + 14 y = 4 + e^{\frac{x}{2}}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{2}{7} + \frac{4}{55} e^{\frac{x}{2}}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + 14 y = 4 + e^{\frac{x}{2}}

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{2}{7} + \frac{4}{55} e^{\frac{x}{2}}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{2}{7} + \frac{4}{55} e^{\frac{x}{2}}

y^{^{''}} - 4 y = 32 t

y^{^{''}} - 5 y^{^{'}} + 6 y = - 12 + e^{t}

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 - 4 x^{3}

y^{^{''}} - y = 7 t

y^{^{''}} - 4 y = cos (3 x)