4(d^2y)/(dx^2)-4(dy)/(dx)+3y=0

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 2

y^{^{'''}} + 4 y^{^{''}} + y^{^{'}} - 26 y = 0, y (0) = e^{2 x}

y^{^{''}} - 2 y^{^{'}} = - 4 y

7 y^{^{''}} - 8 y^{^{'}} + y = 0

60 x^{^{''}} + 240 x = 0, x (0) = 0, x^{^{'}} (0) = - 8