y^{''}-(4y^')/3+(97y)/(36)=0

Lösung

y^{^{''}} - \frac{4 y ^{^{'}}}{3} + \frac{97 y}{36} = 0

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Schritte zur Lösung

y^{''} (t) - \frac{4 y ^{'} ( t )}{3} + \frac{97 y}{36} = 0

Solve linear ODE:

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = \frac{31}{2}

4 \frac{d y}{d x} - 3 \frac{d ^{2} y}{d x ^{2}} = 0

y^{^{'''}} + 5 y^{^{''}} - 11 y^{^{'}} - 39 y = 0

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{^{''''}} + 5 y^{^{''}} - 36 y = 0