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

解

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}

解答ステップ

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

分離可能 ODE を解く:

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}