Problem: Consider the differential equation: y\' = 2y - (y^2) , (E) (i) Find the

Question

Problem: Consider the differential equation:
y' = 2y - (y^2) ,    (E)
(i) Find the critical (equilibrium points;
(ii) Sketch the graph of the solutions;
(iii) Solve the initial value problem (E) with y(0)=-1/2 .
NOTE: please use substitution and an integral factor to solve for the general and exact solution.
Problem: Consider the differential equation:
y' = 2y - (y^2) ,    (E)
(i) Find the critical (equilibrium points;
(ii) Sketch the graph of the solutions;
(iii) Solve the initial value problem (E) with y(0)=-1/2 .
NOTE: please use substitution and an integral factor to solve for the general and exact solution.

Explanation / Answer

All the commands between the lines starting “for” and “end” are repeated with n being given the value 1 the first time through, 2 the second time, and so forth, until n = 8. The subplot constructs a 4 × 2 array of sub-windows and, on the nth time through the loop, a picture is drawn in the nth sub-window. The commands >> x =-1:.05:1;>> for n =1:2:8 subplot (4,2,n), plot (x, sin (n*pi*x)) subplot (4,2,n+1), plot (x, cos(n*pi*x)) end Draw sin npx and cos npx for n = 1, 3, 5, 7 alongside each other. We may use any legal variable name as the “loop counter” (n in the above examples) and it can be made to run through all of the values in a given vector (1:8 and 1:2:8 in the examples). We may also use for loops of the type >> for counter =[23 11 19 5.4 6] ....... end

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.