2x^{''}+10x=0,x(0)=1,x^'(0)=-2

Lösung

2 x^{^{''}} + 10 x = 0, x (0) = 1, x^{^{'}} (0) = - 2

x = cos (5 t) - \frac{2}{5} sin (5 t)

Schritte zur Lösung

2 x^{''} (t) + 10 x = 0

Solve linear ODE:

x = cos (5 t) - \frac{2}{5} sin (5 t)

x = cos (5 t) - \frac{2}{5} sin (5 t)

y^{^{''}} + 12 y^{^{'}} - \frac{25}{4} y = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{''}} + 9 x = 0, x (0) = 5, x^{^{'}} (0) = - 11

y^{^{''''}} + 5 y^{^{'''}} - 2 y^{^{''}} - 3 y^{^{'}} + \frac{1}{2} y = 0

(2 d^{5} - 7 d^{4} + 12 d^{3} + 8 d^{2}) y = 0

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