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

Lösung

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

y = c_{1} e^{(2 + 7) x} + c_{2} e^{(2 - 7) x} - \frac{8}{113} sin (2 x) - \frac{7}{113} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{(2 + 7) x} + c_{2} e^{(2 - 7) x} - \frac{8}{113} sin (2 x) - \frac{7}{113} cos (2 x)

y = c_{1} e^{(2 + 7) x} + c_{2} e^{(2 - 7) x} - \frac{8}{113} sin (2 x) - \frac{7}{113} cos (2 x)

y^{^{''}} + 4 y^{^{'}} = - 32 (x + 2), y (0) = 0, y^{^{'}} (0) = - 10

3 y^{^{''}} - 4 y^{^{'}} - 5 y = (x^{2} + 1) e^{- x}

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

y^{^{'''}} - 2 y^{^{'}} = 2, y^{^{''}} (0) = - 1

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