y^{'''}=3y^{''}+9(e^{(5x)})+2(cos(x))

Lösung

y^{^{'''}} = 3 y^{^{''}} + 9 (e^{(5 x)}) + 2 (cos (x))

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{9}{50} e^{5 x} - \frac{1}{5} sin (x) + \frac{3}{5} cos (x)

Schritte zur Lösung

y^{'''} (x) = 3 y^{''} (x) + 9 (e^{(5 x)}) + 2 (cos (x))

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{9}{50} e^{5 x} - \frac{1}{5} sin (x) + \frac{3}{5} cos (x)

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{9}{50} e^{5 x} - \frac{1}{5} sin (x) + \frac{3}{5} cos (x)

y^{^{''}} - y^{^{'}} - y = x^{2} - 2

y^{^{''}} - 16 y^{^{'}} = 32 + 45 e^{x}

y^{^{'''}} - 4 y = e^{t} + t, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 1, y (0) = 1, y^{^{'}} (0) = - 1

(D^{2} + 5 D + 4) Y = x^{2} + 7 x + 9