Inferior89 said:Shouldn't it be separable?
[tex]x^2 y'=1-x^2+y^2-x^2 y^2 [/tex]
[tex]x^2 y' = -(x^2-1)(y^2 + 1) [/tex]
[tex]y'/(y^2 + 1) = -(x^2 - 1) / x^2 [/tex]
And go from there.
A first order differential equation is an equation that involves a function, its derivative, and an independent variable. It is called a first order equation because it involves only the first derivative of the function.
First order differential equations are used in many scientific and mathematical applications, such as modeling physical systems, understanding population growth, and solving complex problems in engineering. Therefore, it is common for scientists to need help with these types of equations to accurately and efficiently solve problems.
The general steps for solving a first order differential equation are to separate the variables, integrate both sides, and solve for the unknown function. However, the specific method for solving the equation may vary depending on the type of equation and its initial conditions.
Some common techniques for solving first order differential equations include separation of variables, integrating factors, substitution, and using specific formulas for certain types of equations (e.g. linear, homogeneous, exact).
Yes, some common mistakes to avoid when solving first order differential equations include forgetting to use initial conditions, not simplifying expressions enough, and making errors when integrating or differentiating. It is important to carefully check each step and use algebraic rules accurately when solving these equations.