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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{5} sin (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{5} sin (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{5} sin (x)

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

\frac{d ^{2} y}{d x ^{2}} + 9 y = x e^{2 x} + sin (3 x)

(d^{2} - 4 d + 3) y = 3 e^{x} \cdot cos (x)

D (p) = 1200

y^{^{''}} - 3 y^{^{'}} - 10 y = 2 e^{3 x}