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

Lösung

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} + e^{x} - \frac{1}{8} sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} + e^{x} - \frac{1}{8} sin (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} + e^{x} - \frac{1}{8} sin (2 x)

y^{^{''}} + y^{^{'}} - 6 y = - e^{2 x} + 12 x^{2} + 2 x + 3

y^{^{''}} + 6 y^{^{'}} + 25 x = 0

y^{^{''}} - n^{2} y = \frac{2 cos ( πn ) x}{n}

y^{^{''}} + 8 y^{^{'}} - 2 y = \frac{5}{e ^{3 t}}

y^{^{''}} + 4 y = sin (x), y (0) = 0, y (1) = 0