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

Lösung

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

y = c_{1} + c_{2} e^{- 4 x} + \frac{1}{21} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 x} + \frac{1}{21} e^{3 x}

y = c_{1} + c_{2} e^{- 4 x} + \frac{1}{21} e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{- 2 e ^{2 t}}{t ^{2} + 1}

y^{^{''}} + 7 y^{^{'}} + 10 y = 100 sin (10 t)

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{4 x}