(d^2y)/(dx^2)-4(dy)/(dx)+5y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x))

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

Solve linear ODE:

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x))

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x))

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

y^{^{''}} - y^{^{'}} - 56 y = 0, y (0) = - 5, y^{^{'}} (0) = 5

y^{^{''}} + 36 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{24}{5}

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

y^{^{'''}} - y^{^{''}} - 46 y^{^{'}} - 80 y = 0