The discussion focuses on solving the differential equation y' = (x + xy^2). The user successfully transforms the equation into dy/(1+y^2) = xdx and integrates to find arctan(y) = 0.5x^2 + C. The main challenge lies in simplifying this result to express y explicitly in terms of x. The relationship between the tangent and arctangent functions is highlighted as a key concept for further simplification.
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well remember that if tan(x)=y then arctan(y)=x 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