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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{5 + e ^{x}}

y^{^{''''}} - 4 y^{^{''}} = t^{2} + e^{t}

y^{^{''}} + 3 y^{^{'}} = 2

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{x} - 12

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