ay^'=-by^2-c,y(0)=10

解

a y^{^{'}} = - b y^{2} - c, y (0) = 10

y = \frac{c tan ( - \frac{c b t - a a r c t a n ( 10 \frac{b}{c} )}{a} )}{b}

解答ステップ

a y^{'} (t) = - b y^{2} - c

分離可能 ODE を解く:

y = \frac{c tan ( - \frac{c b t - a a r c t a n ( 10 \frac{b}{c} )}{a} )}{b}

y = \frac{c tan ( - \frac{c b t - a a r c t a n ( 10 \frac{b}{c} )}{a} )}{b}