y^{''}-2y^'-3y=12e^x-9

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 9

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

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 3 y = 12 e^{x} - 9

Solve linear ODE:

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

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

y^{^{''}} + 16 y = cos (4 t)

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

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{5 + e ^{x}}

y^{^{''''}} - 4 y^{^{''}} = t^{2} + e^{t}

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