(dy)/(dx)=(ycos(x))/(1+2y^2),y(0)=1

解答

\frac{d y}{d x} = \frac{y cos ( x )}{1 + 2 y ^{2}}, y (0) = 1

\frac{cos ( x )}{3}

求解步骤

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

常数函数结果为常数

y (0) = 1

= \frac{1 \cdot cos ( x )}{1 + 2 \cdot 1 ^{2}}

乘开

\frac{1 \cdot cos ( x )}{1 + 2 \cdot 1 ^{2}} : \frac{cos ( x )}{3}

= \frac{cos ( x )}{3}

x^{^{'}} = - 5 x

\frac{d y}{d x} - \frac{y}{1 - x ^{2}} = 0

\frac{d y}{d x} = 5 x sec (y)

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

\frac{d y}{d x} = - y, y (0) = 1