y^{'''}-2y^{''}+y^'=3t^2-18

Lösung

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 3 t^{2} - 18

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + t^{3} + 6 t^{2}

Schritte zur Lösung

y^{'''} (t) - 2 y^{''} (t) + y^{'} (t) = 3 t^{2} - 18

Solve linear ODE:

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + t^{3} + 6 t^{2}

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + t^{3} + 6 t^{2}

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0

10 x^{^{''}} + 45 x^{^{'}} + 2500 x = 180 cos (7 π)

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 x

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} - 64 y = 7 e^{8 x}

y^{^{''}} - 11 y^{^{'}} + 24 y = 2, y (0) = 0, y^{^{'}} (0) = 1