SECOND ORDER DIFFERENTIAL EQUATIONS Learning Outcomes Know the

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SECOND ORDER DIFFERENTIAL EQUATIONS Learning Outcomes: • Know the difference between homogeneous and non-homogeneous

SECOND ORDER DIFFERENTIAL EQUATIONS Learning Outcomes: • Know the difference between homogeneous and non-homogeneous Ønon-homogeneous • Be able to solve non-homogeneous second-order differential equations

Solving homogeneous second order differential equations STRATEGY Step 1: Find the complementary function CF

Solving homogeneous second order differential equations STRATEGY Step 1: Find the complementary function CF (General solution of corresponding homogeneous equation) Step 2: Find a particular integral PI (Substituting for and ) Step 3: Write down the general solution

Example: Find the general solution of P 123 given that the particular integral has

Example: Find the general solution of P 123 given that the particular integral has form Step 1: Find the complementary function CF Auxiliary equation real distinct roots Step 2: Find a particular integral PI equate coefficients Step 3: Write down the general solution

Example: Find the general solution of P 124 given that the particular integral has

Example: Find the general solution of P 124 given that the particular integral has form Step 1: Find the complementary function CF Auxiliary equation real distinct roots Step 2: Find a particular integral PI equate coefficients Step 3: Write down the general solution

Example: a) Show that is a particular integral of the differential equation Scholar P

Example: a) Show that is a particular integral of the differential equation Scholar P 147 b) Find the general solution of this equation Page 124 Ex 6 Step 1: PI P Step 2: CF Auxiliary equation real distinct roots Step 3: Write down the general solution