(d^2y)/(dx^2)+k(dy)/(dx)-k^2y=0

Lösung

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

y = c_{1} e^{\frac{x ( - k + 5 k )}{2}} + c_{2} e^{\frac{x ( - k - 5 k )}{2}}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{x ( - k + 5 k )}{2}} + c_{2} e^{\frac{x ( - k - 5 k )}{2}}

y = c_{1} e^{\frac{x ( - k + 5 k )}{2}} + c_{2} e^{\frac{x ( - k - 5 k )}{2}}

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 10, y^{^{'}} (0) = - 9

y^{^{''}} - 4 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} - 4 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 16

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 3, y (0) = - 12

(D^{5} - 6 D^{4} + 9 D^{3}) y = 0