y^{''}-7y^'+6y=sin(x)

Lösung

y^{^{''}} - 7 y^{^{'}} + 6 y = sin (x)

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

Schritte zur Lösung

y^{''} (x) - 7 y^{'} (x) + 6 y = sin (x)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

y^{^{''}} + 7 y^{^{'}} + 6 y = 8

y^{^{''}} - 4 y = 3 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = u_{2} (t), y (0) = 0, y^{^{'}} (0) = 1

(d^{2} + 2 d + 3) y = e^{2} x sin (x) + 3