Question

I. Solve the homogeneous differential equations with the constant coefficient.

a. ? ′′ + 5? ′ + 6? = 0

b. 4? ′′ − 8? ′ + 3? = 0 ? (0) = 2, ? ′ (0) = ½

 II. Solve non-homogeneous differential equations with the indeterminate coefficient method.

a. ?′′ − 3? ′ = 5cos(?)

b. ? ′ ′ + 5? ′ + 2? ′ = 7? 3?

III. Solve non-homogeneous differential equations with the parameter variation method.

a. ? ′′ − 2? ′ + 3? = ? 2? ? 2

b. ? ′′ − ? = 3??(?)

IV. Solve non-homogeneous differential equations by the operator’s method.

a. 3? ′′ + 3? ′ + ? = √?? −?

b. 6? ′′ − 2? ′ + ? = ? 2

Answer 1

The complete solution of given equation is Y=CF+PI

Here CF = Complementary fumction

PI = particular integral

for given equation is homogenious the solution is CF Only PI is zero.

to find complementary function find roots for the equations as like below

as like that the question B) also done as below

for homogenious functions just find roots followed by complementary function. complementary function may change according to roots are obtain as like below table

FOR NON-HOMOGENIOUS FUNCTION THEY ARE MANY WAYS TO SOLVE QUESTION  ACCORDING TO FUNCTION PRESENT IN THE QUESTION AS BELOW TREE-DIAGRAM

BY THE ABOVE PROCEDURE WE CAN ANSWER ALL THE QUESTIONS BUT I DIDN'T HAVE TIME TO DO SOLUTION FOR EACH AND EVERY QUESTION SO I WAS ANSWERED TWO QUESTIONS AND THE PROCEDURE FOR ALL REMAINING QUESTIONS.

EVEN YOU HAVE ANY QUESTIONS COMMENT I WILL REPLY.