Stewart Calculus Section 9.3

1. 9.3 Separable Equations
For some certain types of differential
equations, there exist explicit solution.
A separable equation is a first order
differential equation in which the expression
for the derivative / can be factored as a
function of and a function of :
= ( )· ( )

2. = ( )· ( )
Examples:
=
=
= +

3. = ( )· ( )

4. = ( )· ( )
= ( )
( )

5. = ( )· ( )
= ( )
( )
= ( )
( )

6. = ( )· ( )
= ( )
( )
= ( )
( )
!
ction
i t fu n
An i mplic

7. Ex:
=

8. Ex:
=
=

9. Ex:
=
=
=

10. Ex:
=
=
=
= +

11. Ex:
=
=
=
= +
= +

12. Ex:
=
=
=
= +
= +
= +

13. Ex: = +

14. Ex: = +
= +

15. Ex: = +
= +
=
+

16. Ex: = +
= +
=
+
=
+

17. Ex: = +
= +
=
+
=
+
= +

18. Ex: = +
= +
=
+
=
+
= +
= ( + )