(x+3xy^2)dx+e^{x^2}ydy=0

解答

(x + 3 x y^{2}) d x + e^{x^{2}} y d y = 0

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

求解步骤

(x + 3 x y^{2}) d x + e^{x^{2}} y d y = 0

求解可分离方程:

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

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

\frac{d}{d θ} (r (θ)) r (θ) = 5 - θ^{3} sin (θ)

y^{^{'}} = e^{(2 + 1) x + (1 + 2) y}

0.001 \cdot y^{^{'}} - \frac{y}{0.001} = 0

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

\frac{d p}{d t} = k (600 - p)