y^{''}+7y^'-12y=e^{3x}-2e^x-5x

Lösung

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3 x} - 2 e^{x} - 5 x

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{1}{18} e^{3 x} + \frac{1}{2} e^{x} + \frac{5 x}{12} + \frac{35}{144}

Schritte zur Lösung

y^{''} (x) + 7 y^{'} (x) - 12 y = e^{3 x} - 2 e^{x} - 5 x

Solve linear ODE:

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{1}{18} e^{3 x} + \frac{1}{2} e^{x} + \frac{5 x}{12} + \frac{35}{144}

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{1}{18} e^{3 x} + \frac{1}{2} e^{x} + \frac{5 x}{12} + \frac{35}{144}

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5 x}

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = e^{- t} sin (t)

y^{^{''}} + y^{^{'}} - 30 y = 2 x

y^{^{''}} + 16 y = t^{2} + 1

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