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Popular >

N^'=r-a(N-b)^2

Solution

N^{^{'}} = r - a (N - b)^{2}

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Popular Examples

y^'= 1/2 sqrt(y)cos^2(sqrt(y))

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

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

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

(dh)/(dt)=-3/100 sqrt(h-19)

\frac{d h}{d t} = - \frac{3}{100} h - 19

(dx)/(dt)=50-x/(100),x=3000,t=0

\frac{d x}{d t} = 50 - \frac{x}{100}, x = 3000, t = 0

f^'(x)=f(x)(1+x)

f^{^{'}} (x) = f (x) (1 + x)

Frequently Asked Questions (FAQ)

What is the solution for N^'=r-a(N-b)^2 ?
The solution for N^'=r-a(N-b)^2 is