y^{'''}-12y^{''}+48y^'-64y=9e^{4x}

Lösung

y^{^{'''}} - 12 y^{^{''}} + 48 y^{^{'}} - 64 y = 9 e^{4 x}

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

Schritte zur Lösung

y^{'''} (x) - 12 y^{''} (x) + 48 y^{'} (x) - 64 y = 9 e^{4 x}

Solve linear ODE:

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

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

y^{^{'''}} + 121 y^{^{'}} = tan (11 x)

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

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t)

y^{^{''}} + 6 y = 4 t^{2} - 3, y (0) = 0, y^{^{'}} (0) = - 7

y^{^{''}} + 10 y^{^{'}} + 16 y = 2581 cos (5 x)