Problem
Solve the following differential equation:
Sketch the family of solution curves.
Solution
First we rearrange the terms in the differential equation to separate the variables.
The left side is of the form 1/u, so we guess its antiderivative to be ln(|u|). Check that this is correct:
Now we can integrate both sides and simplify.
Here, we have written C2 in place of eC1, renaming the constant.
Again, we write C in place of (C2)2.
The solution is a parabola. The family of solution curves looks like this: