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

Lösung

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

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + \frac{t ^{4}}{4} + 2 t^{3} + 9 t^{2} + 24 t + e^{t} t^{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + \frac{t ^{4}}{4} + 2 t^{3} + 9 t^{2} + 24 t + e^{t} t^{2}

y = c_{1} + c_{2} e^{t} + c_{3} t e^{t} + \frac{t ^{4}}{4} + 2 t^{3} + 9 t^{2} + 24 t + e^{t} t^{2}

y^{^{''}} + 2 y^{^{'}} + 2 y = 3 t^{2}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + y = sin (x) + 2 cos (2 x)

(d^{2} - 1) y = x^{2}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 4 e^{3 x}

(D^{3} - 7 D - 6) y = e^{2 x} (1 + x)