- #1

Destroxia

- 204

- 7

## Homework Statement

I believe I have solved this differential equation, yet do not know how the book arrived at it's answer...

Solve the differential equation in its explicit solution form.

The answer the book gives is...

## Homework Equations

Separable Differential Equation

## The Attempt at a Solution

dy/dx = x(x^2+1)/(4y^3)

(4y^3)dy = (x^3+x)dx

∫(4y^3)dy = ∫(x^3+x)dx [/B]

**y^4 = 1/4x^4 + 1/2x^2 + c**

**(initial condition, y(0) = -1/sqrt(2))**

(-1/sqrt(2))^(4) = 0 + 0 + c

C = -1/4

...

y^4 = 1/4x^4 + 1/2x^2 - 1/4

y = (1/4x^4 + 1/2x^2 - 1/4)^(1/4)

(-1/sqrt(2))^(4) = 0 + 0 + c

C = -1/4

...

y^4 = 1/4x^4 + 1/2x^2 - 1/4

y = (1/4x^4 + 1/2x^2 - 1/4)^(1/4)

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I've experimented with simplifying this a bit and found a few other ways to express it, but nothing like what the book has written as the answer.