Consider the initial value problem [math], where [math].

Use the differential equation to find the slope of the tangent line to the solution curve [math] at [math].
Slope =

Use the given initial value to find the equation of the tangent line to the solution curve at [math].
[math]

Use the equation of the tangent line that you just found to approximate [math], the value of the solution at [math].
[math]

Assuming that your approximation for [math] is the actual value of [math], use the differential equation to find the slope of the tangent line to [math] at [math].
Slope =

Use the slope that you just found to find an approximate equation of the tangent line to the solution curve at [math].
[math]

Use the equation of the tangent line that you just found to approximate [math], the value of the solution at [math].
[math]