y^{''}-8y^'+16y=16e^{4x}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 e^{4 x}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + 8 x^{2} e^{4 x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = 16 e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + 8 x^{2} e^{4 x}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + 8 x^{2} e^{4 x}

\frac{d ^{3} y}{d x ^{3}} + y = 3 + e^{- x} + 5 e^{2 x}

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 e^{3 x} + 4 x

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

y^{^{''}} + 2 y^{^{'}} + y = 7 + 75 sin (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = (- 4 x^{2} - 4 x + 2) e^{2 x}