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

Lösung

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}

Schritte zur Lösung

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

Solve separable ODE:

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}

(u - 1) d x + (x + ux) d u = 0

2 t (\frac{d y}{d t}) = 6 y

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

\frac{d y}{d x} 2 x y = 1

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