What is the solution for y^{''}-6y^'+8y=0,y^'(0)=0 ?

The solution for y^{''}-6y^'+8y=0,y^'(0)=0 is y=-(c_{2}e^{4t})/2+c_{2}e^{2t}

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

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

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

\frac{1}{8} x^{^{''}} + 16 x = 0

y^{^{'''}} - 27 y^{^{''}} + 243 y^{^{'}} - 729 y = 0

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

y^{^{''}} + 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 8

10 y^{^{''}} + 11 y^{^{'}} + 3 y = 0

What is the solution for y^{''}-6y^'+8y=0,y^'(0)=0 ?
The solution for y^{''}-6y^'+8y=0,y^'(0)=0 is y=-(c_{2}e^{4t})/2+c_{2}e^{2t}