100y^{''}-140y^'+85y=0,y(2)=9,y^'(2)=8

Lösung

100 y^{''} - 140 y^{'} + 85 y = 0

y = e^{\frac{7 t}{10}} (c_{1} cos (\frac{3 t}{5}) + c_{2} sin (\frac{3 t}{5}))

Schritte zur Lösung

100 y^{''} (t) - 140 y^{'} (t) + 85 y = 0

Solve linear ODE:

y = e^{\frac{7 t}{10}} (c_{1} cos (\frac{3 t}{5}) + c_{2} sin (\frac{3 t}{5}))

y = e^{\frac{7 t}{10}} (c_{1} cos (\frac{3 t}{5}) + c_{2} sin (\frac{3 t}{5}))

x^{^{''}} - 6 x = 0

y^{^{''}} + y^{^{'}} - \frac{10}{3} y = 0

x^{^{''}} + 8 x^{^{'}} + 4 x = 0

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = 0

4 y + 9 y^{^{''}} = - 12 y^{^{'}}