y^{'''}+8y^{''}+20y^'=x^2-4

Lösung

y^{^{'''}} + 8 y^{^{''}} + 20 y^{^{'}} = x^{2} - 4

y = c_{1} + e^{- 4 x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{x ^{3}}{60} - \frac{x ^{2}}{50} - \frac{189 x}{1000}

Schritte zur Lösung

y^{'''} (x) + 8 y^{''} (x) + 20 y^{'} (x) = x^{2} - 4

Solve linear ODE:

y = c_{1} + e^{- 4 x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{x ^{3}}{60} - \frac{x ^{2}}{50} - \frac{189 x}{1000}

y = c_{1} + e^{- 4 x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{x ^{3}}{60} - \frac{x ^{2}}{50} - \frac{189 x}{1000}

y^{^{''}} - 4 y^{^{'}} - 21 = 0

y^{^{''}} + 7 y^{^{'}} + 6 y = sin (2 t), y (0) = 1, y^{^{'}} (0) = 0

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

y^{^{''}} + y^{^{'}} = e^{t} \cdot cos (t)

y^{^{''}} - (2 + 1)^{2} y = e^{28 t} + sin (2 + 1) t