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

Lösung

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

y = (\frac{1}{2} - \frac{3}{4}) e^{2 t} + \frac{3}{4} e^{t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = (\frac{1}{2} - \frac{3}{4}) e^{2 t} + \frac{3}{4} e^{t}

y = (\frac{1}{2} - \frac{3}{4}) e^{2 t} + \frac{3}{4} e^{t}

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

y^{^{''}} + 8 y^{^{'}} + 32 y = 0, y^{0} = 1, y^{^{'}} 0 = - 4