(dy)/(dt)=(te^t)/(ysqrt(6+y^2))

解

\frac{d y}{d t} = \frac{t e ^{t}}{y 6 + y ^{2}}

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6

解答ステップ

\frac{d y}{d t} = \frac{t e ^{t}}{y 6 + y ^{2}}

分離可能 ODE を解く:

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6