- #1
Hydrolyziz
- 6
- 0
Solve this differential equation:
xy'+y=x^2y^2
I've tried using the z subst. Nothing works so far. Any help would be great
xy'+y=x^2y^2
I've tried using the z subst. Nothing works so far. Any help would be great
Difficult differential equation
- Thread starter Hydrolyziz
- Start date
In summary, the differential equation xy'+y=x^2y^2 can be solved by dividing by y² and using a substitution method. Dividing by a function of x will allow for integration and ultimately solve the equation.
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Welcome to PF!
Hi Hydrolyziz! Welcome to PF!
(have a squared: ²)
Divide by y² to give:
xy'/y² + 1/y = x² , and carry on from there.
(Hint: if the LHS was xy'/y² - 1/y, would you be able to integrate it?
divide by some function of x so that you can use a similar method)
Hydrolyziz said:
Hi Hydrolyziz! Welcome to PF!
(have a squared: ²
)Divide by y² to give:
xy'/y² + 1/y = x² , and carry on from there.
(Hint: if the LHS was xy'/y² - 1/y, would you be able to integrate it?
divide by some function of x so that you can use a similar method
)What is a "difficult differential equation"?
A "difficult differential equation" is a mathematical equation that involves one or more derivatives of an unknown function. These equations can be challenging to solve because they often have complex and non-linear relationships between the variables.
What makes a differential equation difficult?
Differential equations can be difficult for a variety of reasons. Some equations may involve multiple variables, non-linear relationships, or complex initial conditions. Additionally, the methods used to solve differential equations can vary depending on the specific equation, making them challenging to solve.
How do you solve a difficult differential equation?
Solving a difficult differential equation often involves using a combination of mathematical techniques, such as separation of variables, integrating factors, or series expansions. The specific method used will depend on the type of equation and the initial conditions given.
What are some real-world applications of difficult differential equations?
Differential equations are used in a variety of scientific fields, including physics, engineering, economics, and biology. They are used to model complex systems and predict how they will change over time. Examples of real-world applications include modeling population growth, predicting the spread of diseases, and understanding the behavior of electrical circuits.
Are there any tips or tricks for solving difficult differential equations?
There are several strategies that can be helpful when solving difficult differential equations. These include trying to simplify the equation by using substitutions or transformations, breaking the problem into smaller, more manageable parts, and checking your solution for validity. It can also be helpful to practice solving various types of differential equations to become more familiar with the techniques involved.
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