My calculus book says the equation: y' + x^2y = y^2 is

Beverley Rahman

Beverley Rahman

Answered question

2022-02-23

My calculus book says the equation:
y+x2y=y2
is not linear.
Linear equations must be of the form:
y+P(x)y=Q(x)
Is the equation not in this form with Q(x) = 0?

Answer & Explanation

Rosalind Barker

Rosalind Barker

Beginner2022-02-24Added 7 answers

A simple argument (among many others) to show that it is not a linear equation is the following. You should have
x2yy2=P(x)yQ(x)
and so
(x2yP(x))y=Q(x).
Since the right-hand side does not depend on y, we must have x2yP(x)=0, but then y=x2P(x), which is impossible.

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