(dy)/(dx)=((x-1)^2)/(3y)

解答

\frac{d y}{d x} = \frac{( x - 1 ) ^{2}}{3 y}

y = \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}

求解步骤

\frac{d y}{d x} = \frac{( x - 1 ) ^{2}}{3 y}

求解可分离方程:

y = \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}

y = \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 6 x ^{2} + 6 x + c _{1}}{3}

\frac{d x}{x ^{2} y} = \frac{d y}{2 y ^{2}}

y^{^{'}} + 14 x y = 0

y y^{^{'}} e^{y^{2}} = x - 1

y^{^{'}} = - y cos (x)

y^{^{'}} - 2 t y^{3} = 0, y (2) = 1