5000x^{''}+105324.07x=0

Lösung

5000 x^{^{''}} + 105324.07 x = 0

x = c_{1} cos (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}}) + c_{2} sin (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}})

Schritte zur Lösung

5000 x^{''} (t) + 105324.07 x = 0

Solve linear ODE:

x = c_{1} cos (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}}) + c_{2} sin (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}})

x = c_{1} cos (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}}) + c_{2} sin (\frac{10532407 t}{125 \cdot 2 ^{\frac{5}{2}}})

81 y^{^{''}} - 36 y^{^{'}} + 8 y = 0

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 10 y = 0

y^{^{''}} + 10 y^{^{'}} + 34 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

x^{^{''}} - 26 x^{^{'}} + 25 x = 0, x (0) = - 1, x^{^{'}} (0) = 2