Please solve this differential equation x+yy' =3y^2y'\sqrt{x^2+y^2}

Zack Wise

Zack Wise

Answered question

2022-04-23

Please solve this differential equation
x+yy=3y2yx2+y2

Answer & Explanation

veceritzpzg

veceritzpzg

Beginner2022-04-24Added 16 answers

Step 1
After rendering v=x2+y2 you have
v 2=3vy2y
Divide by v, and then
v'2v=3y2y'
Step 2
Converting the derivatives to differentials by multiplying by dx then gives
dv2v=3y2 dy 
which is easy to integrate. Remember to include the constant of integration. To get a relation between x and y, put back v=x2+y2 after doing the integration.

Do you have a similar question?

Recalculate according to your conditions!

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?