x^{''}+16x=0,x(0)=0,x^'(0)=5

Lösung

x^{^{''}} + 16 x = 0, x (0) = 0, x^{^{'}} (0) = 5

x = \frac{5}{4} sin (4 t)

Schritte zur Lösung

x^{''} (t) + 16 x = 0

Solve linear ODE:

x = \frac{5}{4} sin (4 t)

x = \frac{5}{4} sin (4 t)

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

{\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 20 y}^{2} = 0

3 y^{^{'''}} + 17 y^{^{''}} + 31 y^{^{'}} + 14 y = 0

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

\frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{2} y}{d x ^{2}} + y = 0