Solving Separable Differential Equations

And if they are not separable, you're going to be taking a class called "differential equations." Solving differential equations means you're going to integrate, and separable equations means you're going to be able to separate and integrate. In some cases they will not already be separated. Solve each of the following:

1) (dy/dx) = x^2 - 3

2) (dy)/(dx) = y^2 + 3
1/(y^2 + 3) dy = dx
And this is, in actuality, an arctangent problem (trigonometric substitution).

3) (dy)/(dx) = 3xy - x
Factor out an x, move the 3y-1 over, and then you have a u-substitution, and it turns out to be du=3, and then you have a (1/3) integral (1/u)du. And to continue doing this problem, you have to remember that e^{a+b} is the same as e^{a}e^{b} so that you can better write this out.

4) y' = 2y/x

y = C_{2}x^{2}

Homework.

Separable differential equations
Math notebook on SDEs
Paul's online math notes re: SDEs
Wikipedia article (click for ODEs)