y^{''}-16y^'=32+45e^x

Lösung

y^{^{''}} - 16 y^{^{'}} = 32 + 45 e^{x}

y = c_{1} e^{16 x} + c_{2} - 2 x - 3 e^{x}

Schritte zur Lösung

y^{''} (x) - 16 y^{'} (x) = 32 + 45 e^{x}

Solve linear ODE:

y = c_{1} e^{16 x} + c_{2} - 2 x - 3 e^{x}

y = c_{1} e^{16 x} + c_{2} - 2 x - 3 e^{x}

y^{^{'''}} - 4 y = e^{t} + t, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 1, y (0) = 1, y^{^{'}} (0) = - 1

(D^{2} + 5 D + 4) Y = x^{2} + 7 x + 9

y^{^{''}} + 2 y^{^{'}} - 15 y = 7 e^{3 t} + (1 - 2 t) sin (6 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = g (t), y (0) = 8, y^{^{'}} (0) = 6