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

In summary, the conversation discusses a differential equation and a given solution that needs to be shown. The attempt at solving the equation has been unsuccessful and the asker is seeking help. The responder suggests using the given solution to solve the equation and mentions the concept of knowing the solution to solve a differential equation.
  • #1
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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?
 
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  • #2
jowjowman said:

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?
 
  • #3
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:
 
  • #4
Thanks HallsofIvy, you saved my day.
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model various natural phenomena in science and engineering.

2. Why is solving a differential equation problem important?

Solving a differential equation problem allows us to understand and predict the behavior of systems in the natural world. It is crucial in many fields, including physics, engineering, and biology.

3. What is the process for solving a differential equation problem?

The process for solving a differential equation problem involves identifying the type of equation, finding a solution using various methods such as separation of variables or substitution, and then verifying the solution by plugging it back into the original equation.

4. What are some common challenges in solving a differential equation problem?

Some common challenges in solving a differential equation problem include identifying the correct type of equation, choosing the appropriate method for solving, and dealing with complex or non-linear equations.

5. What resources are available for help with solving a differential equation problem?

There are many resources available for help with solving a differential equation problem, including textbooks, online tutorials, and software programs. Additionally, seeking guidance from a math tutor or professor can also be helpful.

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