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}

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