(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

1> g(x) = sin x

solving i get :

y_{c}= ec_{1}sin2x + ec_{2}cos2x

US set of sin x = {sinx, cosx} so y_{p}= Asinx + Bcosx

solving i get:

y_{p}= (1/3)sinx

so

y = ec_{1}sin2x + ec_{2}cos2x + (1/3)sinx ...(1)

for the conditions given i get:

c_{1}= 5/6e & ec_{2}= 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 m_{1}= 2i & m_{2}= -2i

y = ec_{1}sin2x +ec_{2}cos2x ....(3)

solving for the conditions giver we get:

c_{1}= 1/ e = c_{2}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 plz.

note that the exercise is long enough to post all the details of the attempt of solution. i hope u reply. thx

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# Homework Help: Help needed in solving an IVP D.E. over 2 intervals

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