(dy)/(dx)y=x^2+2x+3

解答

\frac{d y}{d x} y = x^{2} + 2 x + 3

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

求解步骤

\frac{d y}{d x} y = x^{2} + 2 x + 3

求解可分离方程:

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

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

x^{^{'}} = x^{100} (t^{2} - 1) (t^{2} - 9), x (0) = 1

y^{^{'}} = 2 x y^{2}, y (2) = 1

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

\frac{d y}{d x} = \frac{5 x y}{( ln ( y ) ) ^{6}}

2 q^{^{'}} + 6 q = 2