(d^2y)/(dx^2)-12(dy)/(dx)+32y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 32 y = 0

y = c_{1} e^{8 x} + c_{2} e^{4 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 32 y = 0

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{4 x}

y = c_{1} e^{8 x} + c_{2} e^{4 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = \frac{1}{4}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y (- 1) = 9

y^{^{'''}} - 14 y^{^{''}} + 51 y^{^{'}} - 54 y = 0

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

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