(d^2-4d+3)y=2xe^{3x}+3e^xcos(2x)

Lösung

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

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2} - e ^{3 x} x}{2} - \frac{3}{8} e^{x} sin (2 x) - \frac{3}{8} e^{x} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2} - e ^{3 x} x}{2} - \frac{3}{8} e^{x} sin (2 x) - \frac{3}{8} e^{x} cos (2 x)

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2} - e ^{3 x} x}{2} - \frac{3}{8} e^{x} sin (2 x) - \frac{3}{8} e^{x} cos (2 x)

x^{^{''}} + 6 x^{^{'}} + 23 x = 8 cos (4 t)

y^{^{''}} - 7 y^{^{'}} + 12 y = 4 e^{x}

4 y^{^{''}} + 36 y = csc (x)

y^{^{''}} - 2 y^{^{'}} + y = x e^{x} + 4, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 6 y = u^{2} (t), y (0) = 0