y^{''}-4y+4=-5e^{3x}

Lösung

y^{^{''}} - 4 y + 4 = - 5 e^{3 x}

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

Schritte zur Lösung

y^{''} (x) - 4 y + 4 = - 5 e^{3 x}

Solve linear ODE:

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

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

x^{^{''}} + 4 x = cos (4 t)

x^{^{''}} - 2 x^{^{'}} + 3 x + 2 = 0

y^{^{''}} - 10 y^{^{'}} + 16 = 0

y^{^{''}} + 2 y^{^{'}} + y = 3 x \cdot e^{- x}

y^{^{''}} + 1 y^{^{'}} - 20 y = 1200 t^{3}