(d^2y)/(dx^2)-4(dy)/(dx)-12y=cos(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = cos (x)

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{4}{185} sin (x) - \frac{13}{185} cos (x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = cos (x)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{4}{185} sin (x) - \frac{13}{185} cos (x)

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{4}{185} sin (x) - \frac{13}{185} cos (x)

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

2 y^{^{''}} + 3 y^{^{'}} + y = lo g_{10} (x)

3 y^{^{''}} + 2 g^{2} y = 4.9 g cos (8 t)

x^{^{''}} + 2.8 x^{^{'}} + 4 x = 10, x (0) = 2, x^{^{'}} (0) = 3

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{- 6.5 e ^{- 2 t}}{t ^{2} + 1}