y(dy)/(dx)=3x(y^2+5)^5

解答

y \frac{d y}{d x} = 3 x (y^{2} + 5)^{5}

y = 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5

求解步骤

y \frac{d y}{d x} = 3 x (y^{2} + 5)^{5}

求解可分离方程:

y = 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5

y = 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5, y = - - 4 - \frac{1}{4 ( 3 x ^{2} + c _{1} )} - 5

d y = \frac{y + 9}{x + 8} d x

cos^{3} (y) \frac{d y}{d x} = x csc (y), y (0) = \frac{π}{3}

x y \cdot \frac{d y}{d x} = y - 1

\frac{d v}{d t} = 4 - 8 v

\frac{d y}{d t} = \frac{16 t ^{3}}{y}