5y^{''}-15y=40e^x

Lösung

5 y^{^{''}} - 15 y = 40 e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 4 e^{x}

Schritte zur Lösung

5 y^{''} (x) - 15 y = 40 e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 4 e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 4 e^{x}

y^{^{''}} + 6 y^{^{'}} + 10 y = e^{- 3 t}, y (0) = 4, y^{^{'}} (0) = 5

y^{^{'''}} = 3 y^{^{''}} + 9 (e^{(5 x)}) + 2 (cos (x))

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

y^{^{''}} - 16 y^{^{'}} = 32 + 45 e^{x}

y^{^{'''}} - 4 y = e^{t} + t, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0