Question

The solution of the differential equation x squared y apostrophe apostrophe plus 3 x y apostrophe plus y equals 0 is

Answer 1

is the equation

a2y3ry y = 0

Let so that

y=x y'= mx", /=m(m 1)2 m-2

ry'=mx", y = m(m- 1)x" m

Therefore,

(m2 y"3yy =m(m 1)r 3m m m 3m 1 _

Which equals

y3x (m2 2m +1) (m+1)0

So that (double root)

1,-1 m

Meaning the solutions are

In(a)

General solution is
y(x)C1 c2 In(z) = c1x
for
C2

$\blacksquare$

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