y^{''}+4y^'+5y=1-5x+8(cos(x)-sin(x))

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 1 - 5 x + 8 (cos (x) - sin (x))

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

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 1 - 5 x + 8 (cos (x) - sin (x))

Solve linear ODE:

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

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

4 x^{^{''}} - 4 x^{^{'}} + x = \frac{8}{t ^{2}} e^{\frac{t}{2}}

- y^{^{''}} + 2 y^{^{'}} + 3 y = 1

y^{^{''}} - y^{^{'}} = e^{x} (3 sin (x) + cos (x))

4 \frac{d ^{2} y}{d x ^{2}} + 9 y = 15

y^{^{''}} - y = sin (t), y (0) = 0, y^{^{'}} (0) = 0