(d^2y)/(dx^2)-6(dy)/(dx)+8y=3cos(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 6 y = t + e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = 68 cos (3 x)

x^{^{''}} - 9 x - 1 = 0

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