What is the solution for (dx)/(dt)t+t/2 (d^2x)/(dt^2)=0 ?

The solution for (dx)/(dt)t+t/2 (d^2x)/(dt^2)=0 is x=c_{1}+c_{2}e^{-2t}

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(dx)/(dt)t+t/2 (d^2x)/(dt^2)=0

\frac{d x}{d t} t + \frac{t}{2} \frac{d ^{2} x}{d t ^{2}} = 0

x = c_{1} + c_{2} e^{- 2 t}

Solution steps

\frac{d x}{d t} t + \frac{t}{2} \frac{d ^{2} x}{d t ^{2}} = 0

Solve linear ODE:

x = c_{1} + c_{2} e^{- 2 t}

x = c_{1} + c_{2} e^{- 2 t}

4 y^{^{''}} + \frac{1}{4} y^{^{'}} + y = 0

y^{^{''}} + 2 y^{^{'}} - 15 y = 0, y (0) = x, y^{^{'}} (0) = 20

3 y^{^{''}} + 2 y^{^{'}} + 1 y = 0

\frac{y ^{^{''}}}{8} + 3 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = - 5

y^{^{''}} + 4 y = 0, y (0) = 6, y^{^{''}} (0) = - 4

What is the solution for (dx)/(dt)t+t/2 (d^2x)/(dt^2)=0 ?
The solution for (dx)/(dt)t+t/2 (d^2x)/(dt^2)=0 is x=c_{1}+c_{2}e^{-2t}