y^{'''}-5y^{''}+6y^'=0+6sin(x)

Lösung

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 0 + 6 sin (x)

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

Schritte zur Lösung

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 0 + 6 sin (x)

Solve linear ODE:

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

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

y^{^{''}} + y = sin (x), y^{^{'}} (\frac{π}{2}) = \frac{3}{2}, y (0) = 0

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = tan (x)

3 x^{^{''}} + 25 x^{^{'}} + 48 x = 5 cos (4 t)

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 39 x e^{x}