y^{''}+3y^'-7y=t^4e^t

Lösung

y^{^{''}} + 3 y^{^{'}} - 7 y = t^{4} e^{t}

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - 7 y = t^{4} e^{t}

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

x^{^{''}} - 16 x^{^{'}} + 64 x = t e^{8 t}

0.5 y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 t} (4 t - 2)

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{2 t} - 2 t

x^{^{''}} + 36 x = 8 cos (6 t)

y^{^{''}} - 3 y^{^{'}} + 2 y = 7 x + 28