y^{''}-5y^'=5e^{5x}

Lösung

y^{^{''}} - 5 y^{^{'}} = 5 e^{5 x}

y = c_{1} e^{5 x} + c_{2} + e^{5 x} x

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) = 5 e^{5 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} + e^{5 x} x

y = c_{1} e^{5 x} + c_{2} + e^{5 x} x

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{4 t}

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

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

y^{^{'''}} + 25 y^{^{'}} = tan (5 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = - 8