You are being asked to solve the IVP:
where
What kind of ODE is this?
the growth of an insect is studied.The rate of death is proportional to the number of insects,x, (in thousands)at any time, t days after the start of the experiment.rate of birth is proportional to x square.When x=2,no. of larvae hatched equals no. of insects that died. show dx/dt = ax(x-2), where a is a constant. Given that x=a initially,find an equation relating x,a and t where x,a>2.
I can do the show part,but cant figure out the eqn.:S
yes, I had done it in the past.
Set up: B/(x-2)+F/x=1/x(x-2)
2. Multiply the x(x-2) both sides: B/(x-2)+F/x=1/x(x-2)
3. plug in values of x to solve the B and F in the equation: Bx+F(x-2)=1
4. Use the values to finish the integration. Before you solve the equation in terms of t. Plug-in the intial value of the problem and solve for the constant. Then solve the equation in terms of t or let it be in implicit form.
they are just constants variable for the partial fractions. I need to use different variables to what solve the constant variable; I could pick any letter of the alphabet if i desire.
Yes, you may use any character, even those not in the alphabet, such as a smiley face or a heart, but what I mean is what numeric value did you obtain for them? How did you rewrite the expression to be integrated using partial fractions?