# Solving $dx/dt=0.2x^2left(1-x/3right)$ for the initial condition $x(0)=x_0$

I am trying to solve the system $$frac{dx}{dt}=0.2x^2left(1-frac{x}{3}right),$$ if $$x(0)=x_0$$. This is a separable ODE, and my attempt is below.
begin{align} frac{dx}{dt}&=0.2x^2left(1-frac{x}{3}right) \ intfrac{dx}{x^2(3-x)}&=frac{1}{15}int dt \ int frac{1/9}{x}+frac{1/3}{x^2}+frac{1/3}{3-x} dx&=frac{1}{15}int dt \ frac{1}{9}ln(x)-frac{1}{3x}-frac{1}{3}ln(3-x)&=frac{t}{15} +C, Cinmathbb{R}. end{align}
However, I am unsure of how to proceed.

Mathematics Asked on November 21, 2021

This is one of the implicit exuation which means it can be written in a form $$F(x,y)=0$$. As you can see, you cannot do anything more meaningful. All this informations tell us that your solution which you have written at the end is final. Remember that we not always can have solution in a form $$x(t)=ldots.$$

Answered by Novice on November 21, 2021

## Related Questions

### PDF of sufficient statistic of a normal distribution $N(0, theta)$

1  Asked on February 9, 2021 by tanay-mukherjee

### Do you know this finitely presented group on two generators?

1  Asked on February 9, 2021

### Is this a correct way to show that $sum_{k=2}^{infty} frac {1}{sqrt k+k(-1)^k}$ converges?

1  Asked on February 9, 2021 by labbsserts

### Abelian subgroup of prime power index

1  Asked on February 9, 2021 by devendra-singh-rana

### A convex function property

1  Asked on February 9, 2021 by earth

### Real life problem: How many finalists can participate per school?

2  Asked on February 8, 2021 by math2hard

### $displaystylelim_{xto 0}frac{1}{x}int_0^x e^{t^2} dt$

2  Asked on February 8, 2021 by abdul-sami

### Computing $int_{alpha}frac{1}{(z-a)^n(z-b)^m}dz$ using Cauchy integral formula

2  Asked on February 8, 2021 by vic-ryan

### Show that ${x}in mathbb{B}(X)$ for every $xin X$

1  Asked on February 8, 2021 by james2020

### Manifolds Definition

1  Asked on February 8, 2021

### Prove Sylvester Gallai Theorem using combinatorics

0  Asked on February 8, 2021 by devansh-kamra

### Can I assume that “dividing on both sides” as a step in this proof is a well-defined operation?

2  Asked on February 8, 2021 by hugo

3  Asked on February 8, 2021 by sagigever

### Proving $abcd+3geq a+b+c+d$

4  Asked on February 8, 2021

### Sets; is (A∩B)∪C the same as A∩(B∪C)?

1  Asked on February 8, 2021 by user839131

### Doubt in Hoffman and Kunze Linear Algebra Section 8.5

1  Asked on February 8, 2021 by combat-miners

### Convergence in probability from the central limit theorem

2  Asked on February 7, 2021 by secondrate

### Graph theory: strong regular graph

1  Asked on February 7, 2021 by spencer-ireland

### Proving the Fibonacci Recurrence

1  Asked on February 7, 2021

### Find solution of this ODE

1  Asked on February 7, 2021 by ongky-denny-wijaya