(d^2y)/(dx^2)+2y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 y = 0

y = c_{1} cos (2 x) + c_{2} sin (2 x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 y = 0

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x)

x^{^{''}} + 6 x = 0

so l v e f or u, \frac{d ^{2} u}{d t ^{2}} = a u (t)

l in e a r y^{^{''}} - y = 0

y^{^{''''}} - 2 y^{^{'''}} + 10 y^{^{''}} - 18 y^{^{'}} + 9 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = 6, y^{^{'}} (0) = 8