Which of the following sets forms a fundamental set of

Brookee85

Brookee85

Answered question

2022-02-24

Which of the following sets forms a fundamental set of solutions of the linear homogeneous (1+3t)y+9ty9y=0 differential equation:
a.y1=t,y2=2t
b.none of the given answers is true
c.y1=t,y2=e3t
d.y1=2e3t,y2=e3t
e.y1=t2,y2=e3t

Answer & Explanation

Mikayla Swan

Mikayla Swan

Beginner2022-02-25Added 9 answers

Given (1+3t)y+9ty9y=0
(1+3t)y2+9ty9=0
y=9t±(9t)24x(1+3t)(9)2x(1+3t)
y=9t±81t2+36(1+3t)2(1+3t)
y=9t±9(3t+2)22(1+3t)
y=9t±3(3t+2)2(1+3t)
y1=31+3t
y2=9t9t62(1+3t)
y2=18t62(1+3t)=6(1+3t)2(1+3t)=3
y2=3

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