9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=1

Lösung

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y = 2 e^{\frac{2 t}{3}} - \frac{e ^{\frac{2 t}{3}} t}{3}

Schritte zur Lösung

9 y^{''} (t) - 12 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 2 e^{\frac{2 t}{3}} - \frac{e ^{\frac{2 t}{3}} t}{3}

y = 2 e^{\frac{2 t}{3}} - \frac{e ^{\frac{2 t}{3}} t}{3}

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 0

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

x^{^{''}} + x^{^{'}} + \frac{1}{3} x = 0, x (0) = 4, x^{^{'}} (0) = 0