Stuck in solving a (rather simple) differential equation problem.

[jowjowman]

Homework Statement

Equation: dy/dx=x+1/3y^2 where y>0

Homework Equations

I'm to show that (1/2x^2+x+8)^1/3 is a solution

The Attempt at a Solution

Splitting it up in x/3y^2+1/3y^2 has been futile and I'm out of ideas.

Can anyone help me see the light?

 

[HallsofIvy]

Homework Statement

Equation: dy/dx=x+1/3y^2 where y>0

Is this 1+ (1/3)y^2 or 1+ 1/(3y^2) or (x+ 1)/(3y^2)?

Homework Equations

I'm to show that (1/2x^2+x+8)^1/3 is a solution

So you are NOT required to solve the equation? If y= ((1/2)x^2+ x+ 8)^(1/3), what is y'? Of course, y^2= ((1/2)x^3+ x+ 8)^(2/3). Put those into the equation and show that the the equation is satisfied.

The Attempt at a Solution

Splitting it up in x/3y^2+1/3y^2 has been futile and I'm out of ideas.

Can anyone help me see the light?

 

[epenguin]

Yes, like many other problems in math, it is easier to solve a differential equation when you know the solution.

That may seem like cheating, but actually a rather well kept secret is that the only way to solve a differential equation is to know the solution, at least in outline.

Perhaps this concept can be further generalised. :shy:

 

[jowjowman]

Thanks HallsofIvy, you saved my day.