y^{''}-5y^'+6y=x^2

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 6 y = x^{2}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 3

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

y^{^{''}} + 6 y^{^{'}} + 12 y = 763 e^{2 t} cos (7 t)

y^{^{''}} + y = \frac{2}{cos ( x )}, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} + y = 4 x + 10 sin (x)