(ydy)/(dx)+4x^2+6x+1=0

解答

\frac{y d y}{d x} + 4 x^{2} + 6 x + 1 = 0

y = - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}, y = - - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}

求解步骤

\frac{y d y}{d x} + 4 x^{2} + 6 x + 1 = 0

求解可分离方程:

y = - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}, y = - - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}

y = - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}, y = - - \frac{8 x ^{3}}{3} - 6 x^{2} - 2 x + c_{1}

y^{^{'}} = e^{3 x - 4 y}, y (0) = 0

\frac{d y}{d x} + 9 x^{8} y = 0, y = 6 e^{- x^{9}}

e^{y} y^{^{'}} = 1, y (0) = ln (x + c)

y^{^{'}} = x y^{2} sin (x), y (0) = 2

x^{2} y^{^{'}} - 2 y = 0