y^{''}-4y^'+3y=e^{4x}(-8+29x+12x^2)

Lösung

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{4 x} (- 8 + 29 x + 12 x^{2})

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

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 3 y = e^{4 x} (- 8 + 29 x + 12 x^{2})

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 32 sin (2 x) + 16 cos (2 x)

5 y^{^{''}} + y^{^{'}} = - 6 x, y (0) = 0, y^{^{'}} (0) = - 10

y^{^{'''}} + y^{^{'}} = sin (x)

y^{^{''}} + 2 y^{^{'}} + y = \frac{ln ( x )}{e ^{x}}

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