Attempted several times to find out what w(t) is and cannot get it... Some help

Question

Attempted several times to find out what w(t) is and cannot get it... Some help for that would be apprecaited and an explation of how it's done.
As far as I am concerned the Wronskian is the determinant of (y1 and y2) and (y'1 and y'2)
Thanks in advance!!!!

At least one of the answers above is NOT correct. Find the function y1 of t which is the solution of 49y" + 84y' + 35y = 0 with initial conditions y1(0) = 1, y1'(0) = 0. y1 = find the function y2 of t which is the solution of 49y"+ 84y' + 35y = 0 with initial conditions y2(0) = 0, y2'(0) = 1. y2 = Find the Wronskian W(t) = W(y1, y2). W(t) = Remark: You should find that W is not zero and so y1 and y2 from a fundamental set of solutions of 49y" + 84y' + 35y =0.

Explanation / Answer

Your method is absolutely correct but you have multiplied the matrix wrong

matrix multiplication will be

y1*y2' - y2*y1'

y1 = -2.5e^-t + 3.5e^(-5/7)t

y2' = 3.5e^-t - 5/2e^(-5/7)t

y2 = -3.5e^-t +3.5e^(-5/7)t

y1' = 2.5e^-t -5/2e^(-5/7)t

the answer will be

(-2.5e^-t + 3.5e^(-5/7)t)(3.5e^-t - 5/2e^(-5/7)t) - (2.5e^-t -5/2e^(-5/7)t)(-3.5e^-t +3.5e^(-5/7)t)

you had multiplied the minus sign of -3.5 in 2nd function with the minus sign of matrix multiplication. I think you got now :)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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