y^{''}+ay^'+by=0

Lösung

y^{^{''}} + a \cdot y^{^{'}} + b \cdot y = 0

y = c_{1} e^{\frac{t ( - a + a ^{2} - 4 b )}{2}} + c_{2} e^{\frac{t ( - a - a ^{2} - 4 b )}{2}}

Schritte zur Lösung

y^{''} (t) + a \cdot y^{'} (t) + b \cdot y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t ( - a + a ^{2} - 4 b )}{2}} + c_{2} e^{\frac{t ( - a - a ^{2} - 4 b )}{2}}

y = c_{1} e^{\frac{t ( - a + a ^{2} - 4 b )}{2}} + c_{2} e^{\frac{t ( - a - a ^{2} - 4 b )}{2}}

(3440.3669700000000 \dots) y^{^{''}} + (0) y^{^{'}} + (22500) y = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{6}{5}, y^{^{'}} (0) = - 3

y^{^{''}} + 3 y^{^{'}} - 54 y = 0

5 y^{^{''}} + 3 y^{^{'}} + 6 y = 0, y (0) = - 4, y^{^{'}} (0) = 0

y^{^{''''}} + 4 y^{^{''}} + 2 y = 0