What is the solution for y^{''}+(v/a)y^'=0 ?

The solution for y^{''}+(v/a)y^'=0 is y=c_{1}+c_{2}e^{-(vt)/a}

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y^{''}+(v/a)y^'=0

y^{^{''}} + (\frac{v}{a}) y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{v t}{a}}

Solution steps

y^{''} (t) + (\frac{v}{a}) y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{v t}{a}}

y = c_{1} + c_{2} e^{- \frac{v t}{a}}

\frac{d ^{4} y}{d x ^{4}} - 2 (\frac{d ^{2} y}{d x ^{2}}) + y = 0

y^{^{''}} - 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 7 y^{^{'}} = 0, y (0) = 2 - 2 e^{7}, y (1) = 0

\frac{d ^{2} y}{d x ^{2}} + 15 \frac{d y}{d x} + 56 y = 0

y^{^{''}} + 4 y^{^{'}} + k y = 0

What is the solution for y^{''}+(v/a)y^'=0 ?
The solution for y^{''}+(v/a)y^'=0 is y=c_{1}+c_{2}e^{-(vt)/a}