(dy)/(dx)=7-y^2

解答

\frac{d y}{d x} = 7 - y^{2}

y = - \frac{7 e ^{27 x + 27 c_{1}}}{1 - e ^{27 (x + c_{1})}} - \frac{7}{1 - e ^{27 (x + c_{1})}}

求解步骤

\frac{d y}{d x} = 7 - y^{2}

求解可分离方程:

y = - \frac{7 e ^{27 x + 27 c_{1}}}{1 - e ^{27 (x + c_{1})}} - \frac{7}{1 - e ^{27 (x + c_{1})}}

y = - \frac{7 e ^{27 x + 27 c_{1}}}{1 - e ^{27 (x + c_{1})}} - \frac{7}{1 - e ^{27 (x + c_{1})}}

y \cdot y^{^{'}} - 2 x = sin (x), y (0) = 6

\frac{d y}{d x} = \frac{3 y}{2 y ^{2} + 1}, y = 1, x = 3

(t^{2} - 16 t + 15) \frac{d y}{d t} = y

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

y^{^{'}} = x y^{3} (1 + x^{2})^{\frac{1}{2}}