Solve-by-using-change-the-conistant-megbod-4y-y-x-2-1-x-x-

Question Number 93451 by mhmd last updated on 13/May/20

S o l v e b y u s i n g c h a n g e t h e c o n i s t a n t m e g b o d

4 y^{^{″}} + y = \frac{x^{2} - 1}{x \sqrt{x}} ?

Commented by i jagooll last updated on 13/May/20

what is conistant megbod ?

Commented by mhmd last updated on 13/May/20

s o r y m e t h o d n o t m e g b o d

Commented by john santu last updated on 13/May/20

characteristic eq : {4 r}^{2} + 1 = 0

r = \pm \frac{1}{2} i . homogenous solution

y_{h} = C_{1} e^{\frac{1}{2} i} + C_{2} e^{- \frac{1}{2} i}

y_{h} = C_{1} \cos (\frac{1}{2} x) + C_{2} \sin (\frac{1}{2} x)

Particular solution

y_{p} = \frac{\sqrt{x} - x^{- 3 / 2}}{{4 D}^{2} + 1}