Exercise
- Sketchthe slopefield of the differentialequation. Sketchthe solutioncurvesbasedon it.
- Sketchthe slopefield of the differentialequation. Find the isoclinesand sketcha solution
curvethat passesthrough(1, 0).
DifferentialEquationsand Integration
We beginthe analyticsolutionsof differentialequationswith a simpletype where is a functionof
only. is a functionof. Thenany antiderivativeof is a solutionby the Fundamental
Theoremof Calculus:
.Example 1 Solvethe differentialequation with.
Solution. .Then gives ,i.e. Therefore
.