y^{'''}+3y^{''}+2y^'=x^2+4x+8

Lösung

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = x^{2} + 4 x + 8

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{x ^{2}}{4} + \frac{11 x}{4}

Schritte zur Lösung

y^{'''} (x) + 3 y^{''} (x) + 2 y^{'} (x) = x^{2} + 4 x + 8

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{x ^{2}}{4} + \frac{11 x}{4}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{x ^{2}}{4} + \frac{11 x}{4}

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

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = e^{x}

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

y^{^{''}} - 5 y^{^{'}} - 6 y = 2 cos (3 x) + 4 e^{2 x}

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