What is the general solution of the differential equation xyy'=x^2+1 ?

jhenezhubby01ff

jhenezhubby01ff

Answered question

2022-09-30

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

Answer & Explanation

Giancarlo Phelps

Giancarlo Phelps

Beginner2022-10-01Added 10 answers

The differential equation
x y y = x 2 + 1
is a First Order linear separable Differential Equation which can be solved simply by rearranging and collection term in x on the RHS and term in y on the LHS;

y d y d x = x 2 + 1 x

And now we "separate the variables" to get;

  y   d y =   x + 1 x   d x

Which is trivial to integrate to get:

    1 2 y 2 = 1 2 x 2 + ln | x | + C

y 2 = x 2 + 2 ln | x | + 2 C
y 2 = x 2 + 2 ln | x | + A

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