# Math Help - 1st order differentiation

1. ## 1st order differentiation

dy/dx = x+y^2

Do I use the intergrating factor and if so when I take y^2 to the other side to make it in the form p(x)y is the x just 1

2. p(x)=-1

3. Originally Posted by cerium
dy/dx = x+y^2

Do I use the intergrating factor and if so when I take y^2 to the other side to make it in the form p(x)y is the x just 1
The DE is not linear so integrating factor cannot be used. I suggest you compare the form against other types of DE's you have been taught ....

4. This is a non-trivial DE. Here is WolframAlpha's solution in terms of Bessel functions. My copy of Mathematica Version 4 yields a solution in terms of Airy functions. I should also point out that the substitution

$u=y-\dfrac{x^{2}}{2}$

changes the DE into the Ricatti equation

$u'=\dfrac{x^{4}}{4}+x^{2}u+u^{2}.$

You could do a series solution method.