y^{''}+2y^'+9y=0,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 2 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = e^{- t} cos (2^{1 + \frac{1}{2}} t) + \frac{sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = e^{- t} cos (2^{1 + \frac{1}{2}} t) + \frac{sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2}

y = e^{- t} cos (2^{1 + \frac{1}{2}} t) + \frac{sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2}

3 x^{^{''}} - 7 x^{^{'}} + 4 x = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (ln (2)) = 3, y (0) = 33

y^{^{'''}} - 5 y^{^{''}} + 5 y^{^{'}} + 11 y = 0

36 y^{^{''}} + 108 y^{^{'}} + 97 y = 0, y^{^{'}} (1) = 3, y (1) = 4

x^{^{''}} - x^{^{'}} - 6 x = 0, x (0) = 2, x^{^{'}} (0) = - 1