ay^{''}+by^'+cy=0,y(0)=0

Lösung

a y^{^{''}} + b y^{^{'}} + cy = 0, y (0) = 0

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 41 y = 0, y (0) = 10, y^{^{'}} (0) = 7

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 10 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 5, y^{^{'}} (0) = 26