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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

(d^{3} - 3 d + 2) \cdot y = x + 1

(d^{2} - 8 d + 20) \cdot y = 100 x^{2} - 26 x \cdot e^{x}

(d^{2} + 4 d + 5) \cdot y = e^{- 2 x}

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

(d^{2} - 4) y = x^{2} e^{3} x