Find solution to differential equation(Check answer please)

[Raziel2701]

Homework Statement

$$\frac{dy}{dx}=4y^{3} -81y$$

There is no initial condition, no constant to solve for. C suffices for the answer the professor is looking for.

I've worked through this problem a couple of times now. It's a separable differential equation and to take the integral of one side requires partial fractions.

For the values of A, B and C when solving the partial fractions I got:

$$A=-\frac{1}{81}$$ $$B=\frac{1}{81}$$ $$C=\frac{1}{81}$$

The problem is for extra credit and so I need confirmation on whether or not my following answer is correct.

Homework Equations

**NONE**

The Attempt at a Solution

Here is the solution that I got after checking my work and having done the problem a number of times:

$$y=\pm\sqrt{\frac{-81}{ce^{162x}-4}}$$

Is this right?

 

[HallsofIvy]

That is not what I get. Presumably, you got x as a function of y and then solved for y. What equation did you solve for y?

 

[Raziel2701]

I start by dividing both sides by 4y^3 -81y, and multiplying both sides by dx so that I have the following equation to integrate:

$$\frac{1}{4y^3-81y}dy=dx$$

I take the integral of both sides of the equation and use partial fractions on the left side of it to be able to integrate and break apart the expression into three fractions.

Yes I did solve for y as a function of x. There really was no formula that I used other than the process I have sort of detailed which simply consists of separating the original equation so that I can integrate each side as shown above and just taking it from there.

I don't know what other information I can share. I guess I can write up all my steps, though that's take a while on latex but I'm willing to do it if it would help.

 

[Dick]

I think your solution looks ok.