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Beliebt Rechnen >

y^'=a-by^2

Lösung

y^{^{'}} = a - b y^{2}

Lösung

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

Graph

Beliebte Beispiele

derivative f(x)= 1/(sqrt(x+4))

d er i v a t i v e f (x) = \frac{1}{x + 4}

integral of (2x^2)/(1-6x^3)

\int \frac{2 x ^{2}}{1 - 6 x ^{3}} d x

(\partial)/(\partial y)(xy^3-x^2)

\frac{\partial}{\partial y} (x y^{3} - x^{2})

integral of (5x^4)/(x^5-3)

\int \frac{5 x ^{4}}{x ^{5} - 3} d x

fläche y=x^2-4,y=-2x

a re a y = x^{2} - 4, y = - 2 x