(d^3y)/(dx^3)-12((dy)/(dx))+16y=32x-8

Lösung

\frac{d ^{3} y}{d x ^{3}} - 12 (\frac{d y}{d x}) + 16 y = 32 x - 8

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

Schritte zur Lösung

\frac{d ^{3} y}{d x ^{3}} - 12 (\frac{d y}{d x}) + 16 y = 32 x - 8

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 6 y = 30 - 30 H (t - 4)

y^{^{''}} + 10 y^{^{'}} + 16 y = 3 cos (5 t) + 4 sin (5 t)

2 y^{^{''}} + 2 y = 2 cos^{2} (x)

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4 x}, y (0) = - 2

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- x} sin (x) + x e^{3 x}