What is the solution for u^{''}+2/r u^'=0 ?

The solution for u^{''}+2/r u^'=0 is u(t)=c_{1}+c_{2}e^{-(2t)/r}

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u^{''}+2/r u^'=0

u^{^{''}} + \frac{2}{r} u^{^{'}} = 0

u (t) = c_{1} + c_{2} e^{- \frac{2 t}{r}}

Solution steps

u^{''} (t) + \frac{2}{r} u^{'} (t) = 0

Solve linear ODE:

u (t) = c_{1} + c_{2} e^{- \frac{2 t}{r}}

u (t) = c_{1} + c_{2} e^{- \frac{2 t}{r}}

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

y^{^{''}} - 2 y^{^{'}} - 195 y = 0, y (0) = 10, y^{^{'}} (0) = - 46

y^{^{'''}} + 8 y^{^{''}} + 7 y^{^{'}} = 0

\frac{4}{9.8} y^{^{''}} + 0.4 y^{^{'}} + 4 y = 0

(\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y)^{2} = 0

What is the solution for u^{''}+2/r u^'=0 ?
The solution for u^{''}+2/r u^'=0 is u(t)=c_{1}+c_{2}e^{-(2t)/r}