We know any solution to the d.e. *y*' = 4
has the form *y* = 4*x* + *C*.
If we're to have *y*(1) = 9, then 9 = 4(1) + *C* and so *C* has to equal 5. There's no choice. This means the specific solution to this IVP is *y* = 4*x* + 5.
The usual process for solving IVPs is to - get a general solution by solving the d.e., then
- get a particular solution by using the initial condition(s) to find the constants.
We'll be able to solve more kinds of differential equations later, but we can do some practice ones now by thinking backwards. |