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人気のある微分積分 >

(xy+y^2)y^'=x^2+xy,y(1)=0

解

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

解

y = x^{2} - 1, y = - x^{2} - 1

解答ステップ

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

分離可能 ODE を解く:

y = x^{2} - 1, y = - x^{2} - 1

y = x^{2} - 1, y = - x^{2} - 1

グラフ

人気の例

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

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

ax^'+bx=0,x(0)=e^{rt}

a x^{^{'}} + b x = 0, x (0) = e^{r t}

(4x^5-16x^3-2x)(1-y^2)-2y(x^2-4)y^'=0

(4 x^{5} - 16 x^{3} - 2 x) (1 - y^{2}) - 2 y (x^{2} - 4) y^{^{'}} = 0

derivative of x^2+derivative of y^2=1

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

y^'=(1+x)/(xy),y(1)=-4

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