well remember that if [tex]tan(x)=y[/tex] then [tex]arctan(y)=x[/tex] does this help u? Tan and arctan are inverse functions so, tan(arctan x)=xS[e^x]=f(u)^n;1635559 said:Homework Statement
i'm trying to solve the simple differential equation y'=(x+xy^2)
2. The attempt at a solution
i get dy/(1+y^2)=xdx and then integrate over the whole thing getting the solution
arctan(y)=0.5x^2+C
my problem is how do i simply this down to an equation in the form y=...
i must be missing something
A simple differential equation is an equation that involves a function and its derivatives. It describes the relationship between the function and its derivatives, and is often used to model real-world phenomena.
A simple differential equation is one in which the function and its derivatives are only raised to the first power. In a complex differential equation, the function and its derivatives may be raised to higher powers or may involve multiple variables.
Simple differential equations are used in many fields such as physics, engineering, economics, and biology to model various processes and phenomena. They are particularly useful in predicting the behavior of systems over time.
The solution to a simple differential equation involves finding the function that satisfies the equation. This can be done through various methods, such as separation of variables, substitution, or using an integrating factor.
The order of a simple differential equation is determined by the highest derivative present in the equation. For example, y' = 3x is a first-order simple differential equation, while y'' + 2y' + y = 0 is a second-order simple differential equation.