14y^{''}+y^'+y=x^2-3x

Lösung

14 y^{^{''}} + y^{^{'}} + y = x^{2} - 3 x

y = e^{- \frac{x}{28}} (c_{1} cos (\frac{55 x}{28}) + c_{2} sin (\frac{55 x}{28})) + x^{2} - 5 x - 23

Schritte zur Lösung

14 y^{''} (x) + y^{'} (x) + y = x^{2} - 3 x

Solve linear ODE:

y = e^{- \frac{x}{28}} (c_{1} cos (\frac{55 x}{28}) + c_{2} sin (\frac{55 x}{28})) + x^{2} - 5 x - 23

y = e^{- \frac{x}{28}} (c_{1} cos (\frac{55 x}{28}) + c_{2} sin (\frac{55 x}{28})) + x^{2} - 5 x - 23

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = x^{3} e^{2 x}

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

y^{^{'''}} + 16 y^{^{'}} = e^{- π x}

x^{^{''}} + 4 x = 4 sec^{2} (2 t)

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 2