What is the solution for -10+4x+5(dx)/(dt)=0 ?

The solution for -10+4x+5(dx)/(dt)=0 is x=-(e^{(-4t-c_{1})/5})/(2)+5/2

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-10+4x+5(dx)/(dt)=0

- 10 + 4 x + 5 \frac{d x}{d t} = 0

x = - \frac{e ^{\frac{- 4 t - c _{1}}{5}}}{2} + \frac{5}{2}

Solution steps

- 10 + 4 x + 5 \frac{d x}{d t} = 0

Solve separable ODE:

x = - \frac{e ^{\frac{- 4 t - c _{1}}{5}}}{2} + \frac{5}{2}

x = - \frac{e ^{\frac{- 4 t - c _{1}}{5}}}{2} + \frac{5}{2}

5 x y \frac{d y}{d x} = 2 x, y > 0

\frac{d y}{d x} x^{2} \cdot (1 + y) = y^{2} (x - 1)

x + x y + y^{^{'}} = 0

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (4)

\frac{d y}{d x} = \frac{4 y}{1 + x}

What is the solution for -10+4x+5(dx)/(dt)=0 ?
The solution for -10+4x+5(dx)/(dt)=0 is x=-(e^{(-4t-c_{1})/5})/(2)+5/2