y^{''}=6y^'-8y,y^'(0)=2

Lösung

y^{^{''}} = 6 y^{^{'}} - 8 y, y^{^{'}} (0) = 2

y = \frac{e ^{4 t} ( 1 - c _{2} )}{2} + c_{2} e^{2 t}

Schritte zur Lösung

y^{''} (t) = 6 y^{'} (t) - 8 y

Solve linear ODE:

y = \frac{e ^{4 t} ( 1 - c _{2} )}{2} + c_{2} e^{2 t}

y = \frac{e ^{4 t} ( 1 - c _{2} )}{2} + c_{2} e^{2 t}

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = - 3

5 y^{^{''}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

4 y^{^{''}} + \frac{16}{0.25} y = 0, y (0) = 0

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

y^{^{''}} + 10 y^{^{'}} + 21 y = 0, y (0) = 1, y^{^{'}} (0) = 0