(t^3+7t^3x^2)dt+xe^{t^4}dx=0,x(0)=0

解

(t^{3} + 7 t^{3} x^{2}) d t + x e^{t^{4}} d x = 0, x (0) = 0

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}

解答ステップ

(t^{3} + 7 t^{3} x^{2}) d t + x e^{t^{4}} d x = 0

分離可能 ODE を解く:

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}