Question Number 100327 by bobhans last updated on 26/Jun/20

Solve x^2 y′′−3xy′−5y=0

Commented bybobhans last updated on 26/Jun/20

n(n−1)−3n−5=0  n^2 −4n−5=0, (n−5)(n+1)=0  has roots n=5 ,−1  generall solution •y=C_1 x^5 +C_2 x^(−1)

Answered by mathmax by abdo last updated on 27/Jun/20

am^2  +(b−a)m +c =0 with a=1  ,b =−3  ,c =−5  ⇒m^2  −4m −5 =0 →Δ^′  =4+5 =9 ⇒m_1 =2+3 =5 and m_2 =2−3 =−1 ⇒  y =ax^5  +bx^(−1)

Commented bymathmax by abdo last updated on 27/Jun/20

y =αx^5  +β x^(−1)  =αx^5  +(β/x)