The author of my textbook asks to verify that the

stop2dance3l

stop2dance3l

Answered question

2022-01-20

The author of my textbook asks to verify that the function:
y=23ln(1+x2)+C
solves the differential equation
dydx=x3y+yx3
However, this is an error and this y does not solve the differential equation. Is there a simple typo that makes the problem workable?

Answer & Explanation

temzej9

temzej9

Beginner2022-01-20Added 30 answers

y=23ln(1+x2)+C square both sides and differentiate and you get 2yy=23×2x1+x2
yy=23(1+x2)
y=23y(1+x2)
=23y+3yx2
Cheryl King

Cheryl King

Beginner2022-01-21Added 36 answers

Differentiating
y=23ln(1+x2)+C
With respect to x should lead you to
y(x)=2x6(x2+1)ln(1+x2)
That should help you for
dydx=x3y+yx3
Edit: just saw your comment how the original had an x3 term rather than x2.

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