(d^2f)/(dx^2)=-a^2f(x)

Lösung

\frac{d ^{2} f}{d x ^{2}} = - a^{2} f (x)

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

Schritte zur Lösung

\frac{d ^{2} f}{d x ^{2}} = - a^{2} f

Solve linear ODE:

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

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

(D^{6} + 6 D^{4} + 9 D^{2}) y = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 5

x^{^{'''}} - x^{^{''}} = 0, x (0) = 1, x^{^{'}} (0) = 3, x^{^{''}} (0) = 2

y^{^{''}} - 10 y^{^{'}} + 34 y = 0, y (0) = 5, y^{^{'}} (0) = - 2

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 2