# Can anyone check if my answer for this ODE is correct?

• ronaldor9
In summary, the given equation can be solved by taking the natural logarithm of (4(y-1)^2 + (x-2)^2) and adding 2 times the arctangent of (x-2)/(2y-2). This result differs from the textbook's answer only by a constant. The use of the identity tan(a) = 1/tan(π/2 - a) was discussed, and the correct form of the answer was clarified to include a constant instead of zero.
ronaldor9

## Homework Statement

$$(x+2y-4)\,dx - (2x-4y)\,dy=0$$

## The Attempt at a Solution

$$\mathrm{ln}[4(y-1)^2+(x-2)^2] + 2\mathrm{arctan}\frac{x-2}{2y-2}=C$$
$$\mathrm{ln}[4(y-1)^2+(x-2)^2] - 2\mathrm{arctan}\frac{2y-2}{x-2}=C$$

Last edited:
Hi ronaldor9!

tan(a) = 1/tan(π/2 - a), so theyr'e the same, except for a constant

what were the initial conditions?

Hey, sorry i meant to place a constant instead of the zero.
Does that identity work for arctan?

ronaldor9 said:
Hey, sorry i meant to place a constant instead of the zero.
Does that identity work for arctan?

oh come on

if tan(a) = 1/tan(π/2 - a),

then putting T = tan(a) gives 1/T = tan(π/2 - a),

so arctanT = a = π/2 - arctan(1/T)

Thanks! tiny-tim

## 1. How do I know if my answer for an ODE is correct?

The best way to check if your answer for an ODE is correct is to solve the equation again using a different method or approach. You can also compare your answer to the solutions provided in textbooks or online resources.

## 2. Can I use a calculator to check my ODE answer?

Yes, you can use a calculator to check your ODE answer. However, it is important to make sure that you are inputting the correct equation and using the correct functions on your calculator.

## 3. What should I do if my answer for an ODE is different from the textbook solution?

If your answer for an ODE is different from the textbook solution, it is important to double check your work and make sure there are no errors. If you are still unsure, you can consult with your professor or a tutor for clarification.

## 4. Is it necessary to show all of my work when checking my ODE answer?

Yes, it is important to show all of your work when checking your ODE answer. This allows you to identify any mistakes or errors in your calculations and make corrections.

## 5. What are some common mistakes to watch out for when checking an ODE answer?

Some common mistakes to watch out for when checking an ODE answer include forgetting to include constants of integration, making errors in algebraic manipulations, and using incorrect values or functions in your calculations.

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