Hw7: Problem 5 Previous Problem List Next (1 paint) We consider the initial valu

Question

Hw7: Problem 5 Previous Problem List Next (1 paint) We consider the initial value problem 6x2y"-33zy' + 18y-0, y(1) = 2, y,(1) = 3 By looking for solutions in the form y z"in an Euler Cauchy problem Az2y" + Bzy + Cy = 0, w e obtain a auxiliary equation Ar2 + B A r + -0 which IS the analog of the auxiliary equation in the constant coefficient case (1) For this problem find the auxiliary equation: (2) Find the roots of the auxiliary equation: (3) Find a fundamental set of solutions y1,32 (4) Recall that the complementary solution (Le., the general solution) is Ye = cih + c2y2. Find the unique solution satisfying y(1)-2, 0 (enter your results as a comma separated list) (enter your results as a comma separated list) y' (1) = 3

Explanation / Answer

1.

6r(r-1)-33r+18=0

6r^2-39r+18=0

(2)

6r^2-36r-3r+18=0

6r(r-6)-3(r-6)=0

r=1/2,6

(3)

y1,y2= x^{1/2},x^6

4)

y= C x^{1/2}+D x^6

y(1)=C+D=2,

y'(1)=C/2+6D=3 , C+12D=6

11D=4

D=4/11,C=2-4/11=18/11

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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