y^{''}+y=e^{-t}sin(e^{-t})+cos(e^{-t})

Lösung

y^{^{''}} + y = e^{- t} sin (e^{- t}) + cos (e^{- t})

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t + sin (t) \cdot \int cos (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t

Schritte zur Lösung

y^{''} (t) + y = e^{- t} sin (e^{- t}) + cos (e^{- t})

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t + sin (t) \cdot \int cos (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t + sin (t) \cdot \int cos (t) (e^{- t} sin (e^{- t}) + cos (e^{- t})) d t

y^{^{''}} + y = \frac{x}{∣ x ∣}

(D^{2} + 5 D + 6) y = x^{2} + 2 x

490 y^{^{''}} + 20 y = 8 cos (6 t)

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

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