Question

Find the general solution of the differential equation that is valid in any interval not including the point which is singular.

Answer 1

2 This an x = 0 gereen differential equation is; ? y" + 7xy' +13y = 0 Euder equation and the singular pont į Assieme a solution looks like y=x^ Differentiate, and substitute ento the differential equation : your - rann y"=r(2-1) xr-2 3 y tror +13ar. y' i x²y +72 r ay' + 13 sy (8-1) +7% +13 = 0 = 0

$782-8 + 72 +13= 0 7 r²r6r +13=0 - 6+ -16 z7 r = 2 7 r -6 + 4 2 27 r 2 – 3 + 2 oo L 23 C2 are general solution is, [qcas (2 ln x) + C2 cas (2 enx) + C2 sin (2 ln ag sen (2 en a) where a and arbitrary constants. Since is defined only for 2070 . interreal where the general solution valid is cool which doesnot contain the singular point en a the is 2 20.