x^{''}+6x^'+3x=0,x^'(0)=1,x(0)=2

Lösung

x^{^{''}} + 6 x^{^{'}} + 3 x = 0, x^{^{'}} (0) = 1, x (0) = 2

x = - \frac{( 12 - ( 7 6 - 12 ) ( 3 + 6 ) ) ( 3 + 6 ) e ^{(- 3 + 6) t}}{36} - \frac{7 6 - 12}{12} e^{(- 3 - 6) t}

Schritte zur Lösung

x^{''} (t) + 6 x^{'} (t) + 3 x = 0

Solve linear ODE:

x = - \frac{( 12 - ( 7 6 - 12 ) ( 3 + 6 ) ) ( 3 + 6 ) e ^{(- 3 + 6) t}}{36} - \frac{7 6 - 12}{12} e^{(- 3 - 6) t}

x = - \frac{( 12 - ( 7 6 - 12 ) ( 3 + 6 ) ) ( 3 + 6 ) e ^{(- 3 + 6) t}}{36} - \frac{7 6 - 12}{12} e^{(- 3 - 6) t}

y^{^{'''}} + 3 y + 4 y = 0

y^{^{''}} - a y^{^{'}} + y = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 4, y (0) = 2

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

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (9) = 0