Solving a diff eq by substituion

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In summary, the conversation is about solving the equation x*y2(dy/dx)=y3-x3 and checking the solution for accuracy. The suggested method is to solve for y and then take the derivative and plug it into the equation to check for equality.
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shemer77
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Homework Statement


x*y2(dy/dx)=y3-x3
solve the problem

Homework Equations





The Attempt at a Solution


My answer was (x3/3)+c=y/x
there is no answer in the back of the book for this one so i just want to make sure i got it right
 
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  • #2
shemer77 said:

Homework Statement


x*y2(dy/dx)=y3-x3
solve the problem

Homework Equations



The Attempt at a Solution


My answer was (x3/3)+c=y/x
there is no answer in the back of the book for this one so i just want to make sure i got it right
Solve your result for y. Then, take the derivative & plug it into the given equation. See if you get equality.
 

1. What is substitution in solving a differential equation?

Substitution is a mathematical technique used to solve differential equations by replacing the original variables with new ones in order to simplify the equation and make it easier to solve.

2. When should substitution be used in solving a differential equation?

Substitution is typically used when the differential equation cannot be solved using other methods, such as separation of variables or integration. It is also useful when the equation contains variables that are difficult to work with.

3. What are the steps involved in solving a differential equation by substitution?

The first step is to identify which variable can be substituted in the equation. Then, the new variable is introduced and the original equation is rewritten in terms of the new variable. The next step is to solve the resulting equation and substitute the original variable back in to get the final solution.

4. Are there any limitations to using substitution in solving differential equations?

Yes, there are some limitations to using substitution. It may not always be possible to find a suitable substitution that simplifies the equation. Additionally, the resulting equation after substitution may still be difficult to solve.

5. Can substitution be used to solve all types of differential equations?

No, substitution cannot be used to solve all types of differential equations. It is most effective for solving first-order ordinary differential equations and may not be applicable for higher-order equations or partial differential equations.

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