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

Lösung

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

y = c_{1} e^{3 t} + c_{2} e^{2 t} - 2 + \frac{1}{2} e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{2 t} - 2 + \frac{1}{2} e^{t}

y = c_{1} e^{3 t} + c_{2} e^{2 t} - 2 + \frac{1}{2} e^{t}

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

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

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

y^{^{''}} + 3 y^{^{'}} + 21 y = 9 cos (4 t)

4 y^{^{''}} + 7 y^{^{'}} - y = 15