# Differential Equations : Separation of Variables

5. Let y(x) be the solution to the differential equation

(x2+1)1/2dy - (x/y)dx = 0 satisfying y(31/2) = 3.

Then [y(81/2)]2 =

A. 6 B. 8 C. 10

D. 11 E. 13

https://brainmass.com/math/calculus-and-analysis/differential-equations-separation-variables-33145

#### Solution Preview

Ok, here we can separate the variables to get:

ydy=xdx/sqrt(1+x^2)

Now we can integrate the sides:

The left hand side would be:

y^2/2

For the ...

#### Solution Summary

Separation of Variables is used to solve a Differential Equation. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.

$2.19