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

Lösung

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

y = 3 e^{- \frac{t}{2}} - \frac{e ^{- \frac{t}{2}} t}{2}

Schritte zur Lösung

4 y^{''} (t) + 4 y^{'} (t) + y = 0

Solve linear ODE:

y = 3 e^{- \frac{t}{2}} - \frac{e ^{- \frac{t}{2}} t}{2}

y = 3 e^{- \frac{t}{2}} - \frac{e ^{- \frac{t}{2}} t}{2}

y^{^{''}} + 12 y^{^{'}} + 16 y = 0

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

\frac{d ^{2} y}{d x ^{2}} + 16 \frac{d y}{d x} + 64 y = 0

y^{^{''}} + 14 y^{^{'}} + 64 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(D^{3} - 3 D^{2} - D + 3) y = 0