y^{''}+0.75y^'+0.3y=0,y^'(0)=0

Lösung

y^{^{''}} + 0.75 y^{^{'}} + 0.3 y = 0, y^{^{'}} (0) = 0

y = e^{- \frac{3 t}{8}} \frac{17 c _{2} cos ( \frac{51 t}{8 5} )}{15} + c_{2} sin (\frac{51 t}{8 5})

Schritte zur Lösung

y^{''} (t) + 0.75 y^{'} (t) + 0.3 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{8}} \frac{17 c _{2} cos ( \frac{51 t}{8 5} )}{15} + c_{2} sin (\frac{51 t}{8 5})

y = e^{- \frac{3 t}{8}} \frac{17 c _{2} cos ( \frac{51 t}{8 5} )}{15} + c_{2} sin (\frac{51 t}{8 5})

y^{^{''}} + 10 y^{^{'}} + 23 y = 0

l in e a r y^{^{''}} - 6 y^{^{'}} + 5 y = 0

y^{^{''}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 22

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 15 y = 0

y^{^{''}} - 19 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 1