θ^{''}(t)+(9.8^2)/(80)θ(t)=0

Lösung

θ^{^{''}} + \frac{9. 8 ^{2}}{80} θ = 0

θ (t) = c_{1} cos (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}}) + c_{2} sin (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}})

Schritte zur Lösung

θ^{''} (t) + \frac{9. 8 ^{2}}{80} θ (t) = 0

Solve linear ODE:

θ (t) = c_{1} cos (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}}) + c_{2} sin (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}})

θ (t) = c_{1} cos (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}}) + c_{2} sin (\frac{49 t}{4 \cdot 5 ^{\frac{3}{2}}})

\frac{( \frac{d ^{2} f}{d x ^{2}} )}{f ( x )} = 1

2 y^{^{''}} - 3 y^{^{'}} - 6 y = 0

9 x^{^{''}} - 12 x^{^{'}} + 4 x = 0, x (0) = 1, x^{^{'}} (0) = - 1

y^{^{''}} + y = 0, y^{^{'}} = 5, y (0) = 9

y^{^{''}} = 7 y^{^{'}} + 4 y