f(x)=(x(2x-1))/(f^'(x))

解答

f (x) = \frac{x ( 2 x - 1 )}{f ^{^{'}} ( x )}

f (x) = \frac{4 x ^{3}}{3} - x^{2} + c_{1}, f (x) = - \frac{4 x ^{3}}{3} - x^{2} + c_{1}

求解步骤

f (x) = \frac{x ( 2 x - 1 )}{f ^{'} ( x )}

求解可分离方程:

f (x) = \frac{4 x ^{3}}{3} - x^{2} + c_{1}, f (x) = - \frac{4 x ^{3}}{3} - x^{2} + c_{1}

f (x) = \frac{4 x ^{3}}{3} - x^{2} + c_{1}, f (x) = - \frac{4 x ^{3}}{3} - x^{2} + c_{1}

y^{^{'}} + 2 x y = - 6 x

y^{^{'}} (x)^{2} = 2 y

y - 6 y^{^{'}} + 13 y = 0, y (0) = e^{3} x cos (2 x)

\frac{y ^{^{'}} + y}{x} = 0

2 y^{^{'}} + y + 1 = 0