CK12 Calculus - Single Variable

We can re-statethe problemin termsof a differentialequationthat satisfiesan initialcondition.

with
By integratingthe right side of the differentialequationwe have

as the generalsolution.Substitutingthe conditionthat gives

Hence is theparticularsolutionof the originalequation satis-
fyingtheinitialcondition
Finally, sincewe are interestedin the valuef (-2), we put -2 into our expressionfor f and obtain:

LessonSummary

1. We foundgeneralsolutionsof differentialequations.


2. We usedinitialconditionsto find particularsolutionsof differentialequations.
   ReviewQuestions

In problems#1–3,solvethe differentialequationfor

In problems#4–7,solvethe differentialequationfor giventhe initialcondition.

4. and


5. and