y^{''}-3y^'+2y=5xe^{2x}+10sin(2x)

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 x e^{2 x} + 10 sin (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{2 x} x ^{2}}{2} - 5 e^{2 x} x - \frac{1}{2} sin (2 x) + \frac{3}{2} cos (2 x)

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 2 y = 5 x e^{2 x} + 10 sin (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{2 x} x ^{2}}{2} - 5 e^{2 x} x - \frac{1}{2} sin (2 x) + \frac{3}{2} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{2 x} x ^{2}}{2} - 5 e^{2 x} x - \frac{1}{2} sin (2 x) + \frac{3}{2} cos (2 x)

x^{^{''}} - 2 x^{^{'}} + x = 3 t e^{- t}

y^{^{''}} + (- 8) y^{^{'}} + 20 y = 100 x^{2} - 65 x e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 4

(D^{2} + D - 12) y = x

y^{^{''}} - 8 y^{^{'}} + 16 y = (x - 1) e^{4 x}