y^{'''}-4y^{''}+5y^'-2y=-6ex+10cos(x)

Lösung

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = - 6 e x + 10 cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} + 3 e x + \frac{15 e}{2} + 2 sin (x) + cos (x)

Schritte zur Lösung

y^{'''} (x) - 4 y^{''} (x) + 5 y^{'} (x) - 2 y = - 6 e x + 10 cos (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} + 3 e x + \frac{15 e}{2} + 2 sin (x) + cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} + 3 e x + \frac{15 e}{2} + 2 sin (x) + cos (x)

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = e^{x}

x^{^{''}} - 18 x^{^{'}} + 81 x = t e^{9 t}

x^{^{''}} - 4 x^{^{'}} - 5 x = 2 + e^{- t}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 9 x

y^{^{''}} + 9 y^{^{'}} + 22 y = e^{- 3 x}