y^{''}+4y^'+8y=8x^2+8x+1

Lösung

y^{^{''}} + 4 y^{^{'}} + 8 y = 8 x^{2} + 8 x + 1

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 8 y = 8 x^{2} + 8 x + 1

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

y^{^{''''}} + 2 y^{^{''}} + 1 = 7 sin (t)

(4 d^{2} - 4 d + 1) y = 100

y^{^{''}} - 5 y^{^{'}} + 6 = 0

x^{^{''}} + 2 x^{^{'}} + x = 2 t e^{- t}

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