What is the solution for (x+3t)(dx)/(dt)+3x-t=0 ?

The solution for (x+3t)(dx)/(dt)+3x-t=0 is x=(-6t+sqrt(40t^2+c_{1)})/2 ,x=(-6t-sqrt(40t^2+c_{1)})/2

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(x+3t)(dx)/(dt)+3x-t=0

(x + 3 t) \frac{d x}{d t} + 3 x - t = 0

x = \frac{- 6 t + 40 t ^{2} + c _{1}}{2}, x = \frac{- 6 t - 40 t ^{2} + c _{1}}{2}

Solution steps

(x + 3 t) \frac{d x}{d t} + 3 x - t = 0

Solve exact ODE:

x = \frac{- 6 t + 40 t ^{2} + c _{1}}{2}, x = \frac{- 6 t - 40 t ^{2} + c _{1}}{2}

x = \frac{- 6 t + 40 t ^{2} + c _{1}}{2}, x = \frac{- 6 t - 40 t ^{2} + c _{1}}{2}

\frac{d y}{d x} + \frac{7 y}{x} = - 5 x - 10

\frac{\partial}{\partial x} (9 x^{7} y^{6} + 7 x^{5} y^{8})

(3 x - 4)^{2}

f (x) = \frac{5}{1 + x ^{2}}

n = 1 \sum \infty n e^{- 4 n}

What is the solution for (x+3t)(dx)/(dt)+3x-t=0 ?
The solution for (x+3t)(dx)/(dt)+3x-t=0 is x=(-6t+sqrt(40t^2+c_{1)})/2 ,x=(-6t-sqrt(40t^2+c_{1)})/2