y^{''}-4y=12

Lösung

y^{^{''}} - 4 y = 12

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3

Schritte zur Lösung

y^{''} (t) - 4 y = 12

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3

y^{^{''}} + y = 2 sin (x)

y^{^{''}} + y^{^{'}} - 2 y = 4, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + y = x^{2} + 2

y^{^{''}} + y = sin (3 t)

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