y^{''}+3y^'-y=0,y(1)=2,y^'(1)=0

Lösung

y^{^{''}} + 3 y^{^{'}} - y = 0, y (1) = 2, y^{^{'}} (1) = 0

y = (2 - \frac{13 - 3}{13}) e^{\frac{- 3 t + 13 t + 3 - 13}{2}} + \frac{( 13 - 3 ) e ^{\frac{- 3 t - 13 t + 3 + 13}{2}}}{13}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - y = 0

Solve linear ODE:

y = (2 - \frac{13 - 3}{13}) e^{\frac{- 3 t + 13 t + 3 - 13}{2}} + \frac{( 13 - 3 ) e ^{\frac{- 3 t - 13 t + 3 + 13}{2}}}{13}

y = (2 - \frac{13 - 3}{13}) e^{\frac{- 3 t + 13 t + 3 - 13}{2}} + \frac{( 13 - 3 ) e ^{\frac{- 3 t - 13 t + 3 + 13}{2}}}{13}

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

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0, y (0) = 2

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

y^{^{''}} + 16 y^{^{'}} + 73 y = 0, y (0) = 4

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9