Solve ODE y'(y'+y)=x(x+1) I tried to remove y^{'2} term by differentiate it wrt x an

Kason Chang

Kason Chang

Answered question

2022-04-20

Solve ODE y(y+y)=x(x+1)
I tried to remove y2 term by differentiate it wrt x and then replace value in hope that it will turn out some exact form but got stuck after
2yyyy+y=xx2+1
How i proceed further or my method is wrong ?
Edit: Exact problem
If yx0 is a solution of the differential equation
y(y+y)=x(x+1) then y(x) is given by
1. 1xex
2. 1xex
3. 1+x+ex
4. 1+x+ex

Answer & Explanation

Diya Bass

Diya Bass

Beginner2022-04-21Added 20 answers

The equation can be rewritten as (y)2+yyx2x=0. One can solve y' in terms of y and x. Notice that the above equation is equivalent to (2y)2+2y(2y)4x24x=0=(2y)2+2y(2y)+y2(y2+4x2+4x)=(2y+y)2(y2+4x2+4x),
(2y+y)2=y2+4x2+4x, implying y2(4x2+4x). Notice that 4x2+4x=4x2+4x+11=(2x+1)21, so y21(2x+1)2. This allows us to say that 2y+y=±y2+(2x+1)21.

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?