y^{''}=7y^'-12y,y^'(0)=1

Lösung

y^{^{''}} = 7 y^{^{'}} - 12 y, y^{^{'}} (0) = 1

y = \frac{e ^{4 t} ( 1 - 3 c _{2} )}{4} + c_{2} e^{3 t}

Schritte zur Lösung

y^{''} (t) = 7 y^{'} (t) - 12 y

Solve linear ODE:

y = \frac{e ^{4 t} ( 1 - 3 c _{2} )}{4} + c_{2} e^{3 t}

y = \frac{e ^{4 t} ( 1 - 3 c _{2} )}{4} + c_{2} e^{3 t}

y^{^{''}} + y = 0, y (0) = 2, y^{^{'}} (0) = 1

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

y^{^{''}} + 3 y + 2 y = 0

y^{^{''}} + 20 y^{^{'}} + 10 y = 0

y^{^{''}} - n^{2} y = 0