What is the solution for y^{''}=y^'-2y ?

The solution for y^{''}=y^'-2y is y=e^{t/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))

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

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

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

Solution steps

y^{''} (t) = y^{'} (t) - 2 y

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

What is the solution for y^{''}=y^'-2y ?
The solution for y^{''}=y^'-2y is y=e^{t/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))