- #1
bobmerhebi
- 38
- 0
Homework Statement
y" +4y = g(x) ; y (0) = 1 & y(0) = 2
g(x) =
sinx , 0 [tex]\leq[/tex]x [tex]\leq[/tex] pi/2
0 , x [tex]\succ[/tex] pi/2
Homework Equations
The Attempt at a Solution
1> g(x) = sin x
solving i get :
yc = ec1sin2x + ec2cos2x
US set of sin x = {sinx, cosx} so yp = Asinx + Bcosx
solving i get:
yp = (1/3)sinx
so
y = ec1sin2x + ec2cos2x + (1/3)sinx ...(1)
for the conditions given i get:
c1 = 5/6e & ec2 = 1/e
thus (1) becomes:
y = (5/6)sin2x + cos2x + (1/3)sinx ... (2) for x between 0 & pi/2
2> for g(x) = 0 with x greater than pi/2
we have : y" + 4y = 0
with m1 = 2i & m2 = -2i
y = ec1sin2x +ec2cos2x ...(3)
solving for the conditions giver we get:
c1 = 1/ e = c2 thus
y = sin 2x + cos 2x ... (4)
from here on i can;t figure how to continue to find a solution / y & y' are continuous @ x = pi/2
i need help please.
note that the exercise is long enough to post all the details of the attempt of solution. i hope u reply. thx