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

Lösung

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

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{t} t ^{3}}{6} + \frac{- e ^{t} t ^{2} + e ^{t} t}{2} - \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{t} t ^{3}}{6} + \frac{- e ^{t} t ^{2} + e ^{t} t}{2} - \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{t} t ^{3}}{6} + \frac{- e ^{t} t ^{2} + e ^{t} t}{2} - \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

y^{^{''}} + 16 y = 3, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} = x, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 42 x + 2

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

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{3 x} (2 + 8 x - 12 x^{2})