I am new to the differential equation and I need some ideas how to solve this problem. x

Jase Howe

Jase Howe

Answered question

2022-06-26

I am new to the differential equation and I need some ideas how to solve this problem.
x 2 y = x 2 y 2 2
y = y 2 2 x 2

Answer & Explanation

g2joey15

g2joey15

Beginner2022-06-27Added 21 answers

Let z(x)=xy(x) then
x z = x 2 y + x y = ( x 2 y 2 2 ) + ( x y ) = z 2 + z 2
hence
3 x = 3 z z 2 + z 2 = z z 1 z z + 2 ,
which yields
z 1 z + 2 = c x 3 ,
for some c. Finally, on either one of the halflines bounded by c 1 / 3 (or on the whole real line if c=0),
y ( x ) = 1 x 1 + 2 c x 3 1 c x 3 .

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?