(d^4y)/(dx^4)+4y=cos(2x)

Lösung

\frac{d ^{4} y}{d x ^{4}} + 4 y = cos (2 x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{20} cos (2 x)

Schritte zur Lösung

\frac{d ^{4} y}{d x ^{4}} + 4 y = cos (2 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{20} cos (2 x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{20} cos (2 x)

y^{^{''}} - 10 y^{^{'}} + 24 y = 90 e^{t}

y^{^{''}} + 9 y^{^{'}} = 8 sin (t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 17 = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 3 y = cos (3 x)

y^{^{''}} + 40 y^{^{'}} + 400 y = 100 sin (10 t)