y^{'''}+y^{''}=12x^5

Lösung

y^{^{'''}} + y^{^{''}} = 12 x^{5}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{7}}{7} - 2 x^{6} + 12 x^{5} - 60 x^{4} + 240 x^{3} - 720 x^{2}

Schritte zur Lösung

y^{'''} (x) + y^{''} (x) = 12 x^{5}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{7}}{7} - 2 x^{6} + 12 x^{5} - 60 x^{4} + 240 x^{3} - 720 x^{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{2 x ^{7}}{7} - 2 x^{6} + 12 x^{5} - 60 x^{4} + 240 x^{3} - 720 x^{2}

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{- 3} e^{3 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 x^{2}

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

y^{^{''}} - 4 y^{^{'}} + 5 y = 125 t^{2}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 18 y^{^{'}} + 45 y = e^{2 x} + x