y^{'''}-2y^{''}+y=5+8xe^x

Lösung

y^{^{'''}} - 2 y^{^{''}} + y = 5 + 8 x e^{x}

y = c_{1} e^{x} + c_{2} e^{\frac{( 1 + 5 ) x}{2}} + c_{3} e^{\frac{( 1 - 5 ) x}{2}} + 5 - 4 x^{2} e^{x} - 8 e^{x} x

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) + y = 5 + 8 x e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{\frac{( 1 + 5 ) x}{2}} + c_{3} e^{\frac{( 1 - 5 ) x}{2}} + 5 - 4 x^{2} e^{x} - 8 e^{x} x

y = c_{1} e^{x} + c_{2} e^{\frac{( 1 + 5 ) x}{2}} + c_{3} e^{\frac{( 1 - 5 ) x}{2}} + 5 - 4 x^{2} e^{x} - 8 e^{x} x

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 9

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 7

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 6

y^{^{''}} + 7 y + 6 y = e^{6 x}

9 y^{^{''}} - 6 y^{^{'}} + y = 8