t^'=(2t-1)^3

解

t^{^{'}} = (2 t - 1)^{3}

t (x) = \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}, t (x) = - \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}

解答ステップ

t^{'} (x) = (2 t (x) - 1)^{3}

分離可能 ODE を解く:

t (x) = \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}, t (x) = - \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}

t (x) = \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}, t (x) = - \frac{- \frac{1}{4 ( x + c _{1} )}}{2} + \frac{1}{2}