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First Order

Differential Equatio• LINEAR EQUATIONS

• TEST 1: 23/10 10-11.30 AM

• PRESENTATION CHAPTER 30/9/2015

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3. Linear Equations

+ = , ( ) and are continuous functions of .

No products of the function   (), and its derivatives and nfunction or its derivatives occur to any power other thapower.

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Solution of Linear equations

1. Put the differential equation in the correct initial form. Make scoefficient = 1 + =

2. Find () and evaluate 3. Find the integrating factor

=

4. Multiply everything in the differential equation by the integratand then solve for .

=

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Example + 5 = 2

Coefficient = 1, = 5 and = 2=5 =5 The integrating factor, = , = Multiply with integrating factor = = 2 = = 17 +

= 17 2 +

STEP 1

STEP 2

STEP 3

STEP