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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} + y^{^{'}} = x + 1

y^{^{''}} - 8 y^{^{'}} + 7 y = x

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

2 y^{^{''}} + 4 y^{^{'}} + 7 y = x^{2}