xy^2dx+(x^2y+3y)dy=0,y(1)=1

解答

x y^{2} d x + (x^{2} y + 3 y) d y = 0, y (1) = 1

y = \frac{c _{1}}{x ^{2} + 3}

求解步骤

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

求解可分离方程:

y = \frac{c _{1}}{x ^{2} + 3}

y = \frac{c _{1}}{x ^{2} + 3}

x^{2} y^{2} y^{^{'}} = 1 + x^{2}

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

y^{^{'}} = 2 x y^{2}, y (0) = \frac{1}{4 - x ^{2}}

12 sin (x) \frac{d y}{d x} = 1 ey - ye - y

\frac{d y}{d t} = - a y + b