y^'=y(5x^2+3)

解答

y^{^{'}} = y (5 x^{2} + 3)

y = e^{\frac{5 x ^{3}}{3} + 3 x + c_{1}}

求解步骤

y^{'} (x) = y (5 x^{2} + 3)

求解可分离方程:

y = e^{\frac{5 x ^{3}}{3} + 3 x + c_{1}}

y = e^{\frac{5 x ^{3}}{3} + 3 x + c_{1}}

x + 1 y^{^{'}} = y + 1

(t^{2} - 16 t + 48) (\frac{d y}{d t}) = y

\frac{d z}{d t} = 2 t e^{6 z}

\frac{d}{d x} ((y) \cdot 10) + 5 y = 5

x + y x d x - d y = 0, y^{2} = 4