y^{'''}-2y^{''}+y^'=x^3+2e^x

Lösung

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = x^{3} + 2 e^{x}

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + \frac{x ^{4}}{4} + 2 x^{3} + 9 x^{2} + 24 x + e^{x} x^{2}

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) + y^{'} (x) = x^{3} + 2 e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + \frac{x ^{4}}{4} + 2 x^{3} + 9 x^{2} + 24 x + e^{x} x^{2}

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + \frac{x ^{4}}{4} + 2 x^{3} + 9 x^{2} + 24 x + e^{x} x^{2}

y^{^{''''}} - y^{^{''}} = 2 sin (t) - 3 e^{- t} + 4 t

y^{^{''}} + 4 y = cos (4 t) + 2 sin (4 t)

y^{^{''}} - 4 y = 2 x - 3 cos (x) + e^{- x}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 8 + e^{\frac{x}{2}}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 x} + 4 x - 12