What is the solution for e^2x^'+xe^2+6xx^'=0 ?

The solution for e^2x^'+xe^2+6xx^'=0 is x=(\W(6/(e^{(2e^2-c_{1)+e^2t)/(e^2)}})e^2)/6

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e^2x^'+xe^2+6xx^'=0

e^{2} x^{^{'}} + x e^{2} + 6 x x^{^{'}} = 0

x = \frac{W ( \frac{6}{e ^{\frac{2 e ^{2} - c _{1} + e ^{2} t}{e ^{2}}}} ) e ^{2}}{6}

Solution steps

e^{2} x^{'} (t) + x e^{2} + 6 x x^{'} (t) = 0

Solve separable ODE:

x = \frac{W ( \frac{6}{e ^{\frac{2 e ^{2} - c _{1} + e ^{2} t}{e ^{2}}}} ) e ^{2}}{6}

x = \frac{W ( \frac{6}{e ^{\frac{2 e ^{2} - c _{1} + e ^{2} t}{e ^{2}}}} ) e ^{2}}{6}

\frac{d y}{d x} = 4 y^{- 2} (x^{6} + x^{4} + x^{2})

(A + B) d y = C (\frac{x}{y}) d x

\frac{d y}{d x} = \frac{10 + 12 x}{x y ^{2}}

\frac{d v}{d t} = 60 - \frac{8}{100} v

csc^{3} (x) \frac{d y}{d x} = cos^{2} (y)

What is the solution for e^2x^'+xe^2+6xx^'=0 ?
The solution for e^2x^'+xe^2+6xx^'=0 is x=(\W(6/(e^{(2e^2-c_{1)+e^2t)/(e^2)}})e^2)/6