y^{''}+y^'-2y=x^2+cos(3x)

Lösung

y^{^{''}} + y^{^{'}} - 2 y = x^{2} + cos (3 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- x ^{2} - x}{2} - \frac{3}{4} + \frac{3}{130} sin (3 x) - \frac{11}{130} cos (3 x)

Schritte zur Lösung

y^{''} (x) + y^{'} (x) - 2 y = x^{2} + cos (3 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- x ^{2} - x}{2} - \frac{3}{4} + \frac{3}{130} sin (3 x) - \frac{11}{130} cos (3 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- x ^{2} - x}{2} - \frac{3}{4} + \frac{3}{130} sin (3 x) - \frac{11}{130} cos (3 x)

(d^{2} + 1) y = csc (x)

y^{^{''}} + 1.44 y = 24 cos (1.2 x)

y^{^{''}} + y = 5 e^{- 4 x}, y (0) = 0, y^{^{'}} (0) = 0

6 y^{^{''}} - y^{^{'}} - 2 y = 3 sin (10 x)

y^{^{''}} + y = 10 sin (2 t) + 7 t cos (2 t)