Nonlinear first oder ODE I want to solve the following nonlinear

Madilynn Avery

Madilynn Avery

Answered question

2022-04-21

Nonlinear first oder ODE
I want to solve the following nonlinear ODE
yyx+3y(12x)+1=0.

Answer & Explanation

Yaretzi Odom

Yaretzi Odom

Beginner2022-04-22Added 16 answers

Step 1
Consider the homogeneous equation
yyx+3y(12x)=0
which does not present any problem. Let y=z which gives
x(z6x+3)2z2xz=0z=Cx2+6x2log(x)+3x
Back to y and including the 1 and the variation of parameters, we end with
x2CCx2+6x2log(x)+3x+2=0
which is obviously more than problematic.
RormFrure6h1

RormFrure6h1

Beginner2022-04-23Added 13 answers

Step 1
Let z(x)=1y(x),
so y(x)=z(x)z(x)2,
Step 2
hence -z'(x)z(x)2-1xz(x)+3z(x)(12-x)+1=0,
so z'(x)+z(x)x+3z(x)3(x12)z(x)2=0,
which can be further rewritten as
z'(x)=3(12-x)z(x)3+z(x)2-1xz(x),
which is an Abel equation.

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?