y^{''}+y^'-2y=te^{3t}

Lösung

y^{^{''}} + y^{^{'}} - 2 y = t e^{3 t}

y = c_{1} e^{t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{10} - \frac{7}{100} e^{3 t}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 2 y = t e^{3 t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{10} - \frac{7}{100} e^{3 t}

y = c_{1} e^{t} + c_{2} e^{- 2 t} + \frac{e ^{3 t} t}{10} - \frac{7}{100} e^{3 t}

y^{^{''}} + 24 y^{^{'}} + 144 y = t^{2} e^{- 12 t} + e^{- 12 t}

y^{^{''}} - 81 y = 3

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{2 t}, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 4 y = 4 sin (2 t), y (π) = 0, y^{^{'}} (π) = - 1

y^{^{''}} + 16 y = 12 cos (4 x) + 18 sin (4 x)