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

Lösung

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

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + \frac{1}{24} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + \frac{1}{24} e^{3 x}

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + \frac{1}{24} e^{3 x}

so l v e f or d, d (p) = 480 - 3 p

y^{^{''}} + 4 y = 3 \cdot sin (2 x)

y^{^{''}} - y = 5 x + 2

\frac{d ^{3} y}{d x ^{3}} + y = cos (x)

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