9.3 Separable Equations For some certain types of differential equations, there exist explicit solution. A separable equat...
= ( )· ( )Examples:             =                 =            =        +
= ( )· ( )
= ( )· ( )      = ( )( )
= ( )· ( )      = ( )( )      =   ( )( )
= ( )· ( )      = ( )( )      =   ( )( )                                 !                            ction               ...
Ex:      =
Ex:      =      =
Ex:      =      =      =
Ex:      =      =      =      =   +
Ex:      =      =      =      =   +      =   +
Ex:      =      =      =      =   +      =   +      =   +
Ex:   =   +
Ex:   =   +      =   +
Ex:       =   +          =   +          =      +
Ex:       =   +          =   +          =      +          =      +
Ex:       =   +          =   +          =      +          =      +          = +
Ex:       =   +          =   +          =      +          =      +          = +          =     ( + )
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Calculus II - 14

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Stewart Calculus Section 9.3

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  • Calculus II - 14

    1. 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. 2. = ( )· ( )Examples: = = = +
    3. 3. = ( )· ( )
    4. 4. = ( )· ( ) = ( )( )
    5. 5. = ( )· ( ) = ( )( ) = ( )( )
    6. 6. = ( )· ( ) = ( )( ) = ( )( ) ! ction i t fu n An i mplic
    7. 7. Ex: =
    8. 8. Ex: = =
    9. 9. Ex: = = =
    10. 10. Ex: = = = = +
    11. 11. Ex: = = = = + = +
    12. 12. Ex: = = = = + = + = +
    13. 13. Ex: = +
    14. 14. Ex: = + = +
    15. 15. Ex: = + = + = +
    16. 16. Ex: = + = + = + = +
    17. 17. Ex: = + = + = + = + = +
    18. 18. Ex: = + = + = + = + = + = ( + )

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