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

The solution for (2x+t)(dx)/(dt)+(x-2t)=0 is x=(-t+sqrt(5t^2+c_{1)})/2 ,x=(-t-sqrt(5t^2+c_{1)})/2

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(2x+t)(dx)/(dt)+(x-2t)=0

(2 x + t) \frac{d x}{d t} + (x - 2 t) = 0

x = \frac{- t + 5 t ^{2} + c _{1}}{2}, x = \frac{- t - 5 t ^{2} + c _{1}}{2}

Solution steps

(2 x + t) \frac{d x}{d t} + (x - 2 t) = 0

Solve exact ODE:

x = \frac{- t + 5 t ^{2} + c _{1}}{2}, x = \frac{- t - 5 t ^{2} + c _{1}}{2}

x = \frac{- t + 5 t ^{2} + c _{1}}{2}, x = \frac{- t - 5 t ^{2} + c _{1}}{2}

What is the solution for (2x+t)(dx)/(dt)+(x-2t)=0 ?
The solution for (2x+t)(dx)/(dt)+(x-2t)=0 is x=(-t+sqrt(5t^2+c_{1)})/2 ,x=(-t-sqrt(5t^2+c_{1)})/2