y^{''}-4y^'+4y=0,(1)y=e^{2x}

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, (1) y = e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

y^{^{''}} + 5 y^{^{'}} - 50 y = 0

y^{^{''}} - 440 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3

l in e a r y^{^{''}} + 5 y = 0

x^{^{''}} + 4 x^{^{'}} + 16 x = 0