• dogiipongs
In summary, The problem given is to solve the differential equation y'=-x^2-sin(y). The conversation involves trying to understand the problem and providing assistance without solving it directly. The person has attempted to solve it using the steps for solving a first-order linear differential equation, but it was not successful.
dogiipongs
Question the problem:

y'=-x^2-sin(y)

thank you

What have you tried?

Where are you stuck?

We are willing to help you solve the problem - we are not here to solve it for you.

SammyS said:
What have you tried?

Where are you stuck?
i live in Thailand

We are willing to help you solve the problem - we are not here to solve it for you.

i solve in ODE
step 1. set question dy/dx+P(x)y=g(x)
step 2. P(x)=exp(integrate(F(x))dx)
step 3. x p(x) in 1
but
----->y'=-x^2-sin(y)
----->y'+sin(y)=-x^2 ----1
------>exp(integrate(1)dx
------>exp(x) ----2
x exp(x) in 1

exp(x)y'+exp(x)sin(y)=exp(x)*-x^2 I made ​​up this process safe.
It was not possible to do.ฃ

## 1. How do I solve the equation y'=-x^2-sin(y)?

This is a first-order differential equation that can be solved using separation of variables. Rearrange the equation to have all of the y terms on one side and all of the x terms on the other side. Then, integrate both sides and solve for y.

## 2. What is the general solution to the equation y'=-x^2-sin(y)?

The general solution to this equation is y(x) = -cos(x) + C, where C is a constant of integration. This can be found by integrating both sides of the equation and rearranging to solve for y.

## 3. Can I use a calculator to solve this equation?

No, this equation cannot be solved using a calculator. It requires a knowledge of differential equations and integration techniques.

## 4. Are there any specific techniques for solving this type of differential equation?

Yes, there are specific techniques for solving first-order differential equations such as this one. Separation of variables is a common technique, as well as the use of integrating factors or substitution methods.

## 5. How can I check if my solution to the equation y'=-x^2-sin(y) is correct?

You can check your solution by plugging it back into the original equation. If it satisfies the equation, then it is a valid solution. Additionally, you can also take the derivative of your solution and see if it matches the original equation.

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