We know that the equation *y* = 4*x* + 1
doesn't work because when *x* = 0 we get *y* = 1 instead of *y* = 2. We still want a line with slope 4, but we want it to be 2 when *x* = 0. This sounds like the line *y* = 4*x* + 2
is a good bet. Let's check and see if this works. The derivative is so this function satisfies the d.e. part. When *x* = 0 we get *y* = 4(0) + 2 = 2,
so this function also satisfies the initial condition. That means *y* = 4*x* + 2
is a solution to this initial value problem. It's usually easier to check if the function satisfies the initial condition(s) than it is to check if the function satisfies the d.e., so we recommend checking the initial condition(s) first. |