What is the general solution of the differential equation? : y'=x(1+y^2)

niouzesto

niouzesto

Answered question

2022-09-04

What is the general solution of the differential equation? : y = x ( 1 + y 2 )

Answer & Explanation

detegerex

detegerex

Beginner2022-09-05Added 16 answers

This is a First Order Separable Ordinary Differential Equation. We can rewrite in the form:
1 1 + y 2 d y d x = x
So we can "separate the variables" to get:
  1 1 + y 2   d y =   x   d x
Both integrals are standard calculus results , so integrating we get:
arctan y = 1 2 x 2 + C
Leading to the General Solution:
y = tan ( 1 2 x 2 + C )

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