- #1

Jeff12341234

- 179

- 0

I have a Ti-nSpire CAS. Is there a graphical or other way to check that you have the right answer when solving a D.E. when you CAN'T solve for y?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Jeff12341234
- Start date

In summary, you need to differentiate both sides of the equation to check if it's correct. If it's not, you'll need to use implicit differentiation to solve for y.

- #1

Jeff12341234

- 179

- 0

I have a Ti-nSpire CAS. Is there a graphical or other way to check that you have the right answer when solving a D.E. when you CAN'T solve for y?

Physics news on Phys.org

- #2

SteamKing

Staff Emeritus

Science Advisor

Homework Helper

- 12,811

- 1,672

Your comment is not clear. If you can't solve for Y, how can you check that Y is the right answer?

- #3

Jeff12341234

- 179

- 0

- #4

Mark44

Mentor

- 37,744

- 10,088

It sounds like your solution defines y implicitly as a function of x (or t, or whatever the independent variable is). To check your solution, differentiate both sides of your equation implicitly, and solve for dy/dt, then substitute into your differential equation.Jeff12341234 said:How do you check your answer in a diff. eq. problem when you can't solve for Y?

Jeff12341234 said:I have a Ti-nSpire CAS. Is there a graphical or other way to check that you have the right answer when solving a D.E. when you CAN'T solve for y?

- #5

Jeff12341234

- 179

- 0

Question: tan

Answer: [itex]\frac{1}{2}[/itex]*sin

As far as I know, I need to be able to solve for Y to be able to plug it back into check it. So what do you do when you can't solve for Y?

- #6

Mark44

Mentor

- 37,744

- 10,088

No, and my answer is the same as before. Differentiate both sides of the equation above implicitly, and solve algebraically for dy/dx.Jeff12341234 said:It looks like I will need to provide example to explain the question more clearly.

Question: tan^{3}x*[itex]\frac{y'}{x}[/itex]=(y^{2}+4)sec^{2}x

Answer: [tex]\frac{1}{2}*sin^2(x)-\frac{1}{4y}-\frac{tan^{-1}(y/2)}{8} = c[/tex]

As far as I know, I need to be able to solve for Y to be able to plug it back into check it.

For example, if you ended up with this equation...

x + x

d/dx(x + x

=> 1 + x

Now group all terms that involve dy/dx on one side, and all other terms on the right.

Solve for dy/dx.

See above.Jeff12341234 said:So what do you do when you can't solve for Y?

- #7

Jeff12341234

- 179

- 0

I don't completely follow. I differentiated my answer above in terms of x and got sin(x)*cos(x)=0. If I differentiate it implicitly with y as dependent I get -sin(x)*cos(x)*y^{2}*(y^{2}+4) What do I do with that?

Is there a link to a worked example where they start from an answer similar to what I got, then end up with Y=something, then plug that back into the original D.E. to check it?

Is there a link to a worked example where they start from an answer similar to what I got, then end up with Y=something, then plug that back into the original D.E. to check it?

Last edited:

- #8

Mark44

Mentor

- 37,744

- 10,088

That's incorrect because you didn't differentiate the 1/(4y) and (1/8)tanJeff12341234 said:I don't completely follow. I differentiated my answer above in terms of x and got sin(x)*cos(x)=0.

You differentiated (1/2)sin

d/dx[(1/4)y

When you were learning about derivatives, there should have been a section on implicit differentiation.

I have no idea how you got this.Jeff12341234 said:If I differentiate it implicitly with y as dependent I get -sin(x)*cos(x)*y^{2}*(y^{2}+4) What do I do with that?

The approach you want is applicable only if you have very simple equations in which you can actually solve for y. Many times this is not possible, but you can follow the approach I have suggested throughout this thread - use implicit differentiation. If you don' don't know it, or don't remember learning it, or have forgotten it, look it up.Jeff12341234 said:Is there a link to a worked example where they start from an answer similar to what I got, then end up with Y=something, then plug that back into the original D.E. to check it?

- #9

Jeff12341234

- 179

- 0

Ah, see, that is the problem. I need a way to check my answer even if y isn't solvable. I need a way to know for sure if my general form answer is right.Mark44 said:The approach you want is applicable only if you have very simple equations in which you can actually solve for y. Many times this is not possible, ...

- #10

Mark44

Mentor

- 37,744

- 10,088

Jeff12341234 said:It looks like I will need to provide example to explain the question more clearly.

Question: tan^{3}x*[itex]\frac{y'}{x}[/itex]=(y^{2}+4)sec^{2}x (1)

Answer: [itex]\frac{1}{2}[/itex]*sin^{2}x-[itex]\frac{1}{4y}[/itex]-[itex]\frac{tan^-1(y/2)}{8}[/itex] = c (2)

As far as I know, I need to be able to solve for Y to be able to plug it back into check it. So what do you do when you can't solve for Y?

Jeff12341234 said:Ah, see, that is the problem. I need a way to check my answer even if y isn't solvable. I need a way to know for sure if my general form answer is right.

Using the problem you posted as an example, here's how you check it.

Start with your solution equation - (2), and differentiate it implicitly.

Solve algebraically for dy/dx.

Substitute for dy/dx in the original differential equation - (1). If your solution is correct, you should get an equation that is identically true.

You DON'T need to solve for y in the solution.

There are a few ways to check your answer in a differential equation problem. One method is to plug your answer into the original equation and see if it satisfies the equation. Another approach is to graph both the original equation and your answer to see if they match. Additionally, you can use numerical methods such as Euler's method or Runge-Kutta methods to approximate the solution and compare it to your answer.

Yes, you can use software or calculators to check your answer in a differential equation problem. There are many software programs specifically designed for solving differential equations, such as MATLAB or WolframAlpha. These programs can also graph the solutions and compare them to your answer. However, it is important to also understand the concepts and techniques used to solve differential equations manually.

If your answer doesn't match the solutions provided, there are a few steps you can take to troubleshoot. First, double check your work and make sure you didn't make any mistakes in your calculations. Then, try using a different method to solve the differential equation to see if you get the same answer. You can also ask your teacher or classmates for help or seek out additional resources, such as online tutorials or textbooks, to better understand the problem and solution.

Yes, it is possible to have multiple correct answers for a differential equation problem. This is because differential equations can have families of solutions, meaning there are multiple possible functions that can satisfy the equation. In some cases, the general solution may also include arbitrary constants that can result in a variety of solutions. It is important to understand the concept of general solutions and initial conditions in order to find a specific solution.

If you are still unsure about your answer after checking it, it is best to seek out additional help from your teacher or a classmate. You can also consult online resources or textbooks for further explanations and examples. It is important to fully understand the concepts and techniques used in solving differential equations in order to confidently check your answers and solve future problems.

- Replies
- 4

- Views
- 1K

- Replies
- 6

- Views
- 1K

- Replies
- 3

- Views
- 3K

- Replies
- 2

- Views
- 3K

- Replies
- 3

- Views
- 2K

- Replies
- 16

- Views
- 3K

- Replies
- 6

- Views
- 2K

- Replies
- 2

- Views
- 2K

- Replies
- 3

- Views
- 2K

- Replies
- 65

- Views
- 3K

Share: