Question

differential equations

Solve the given differential equation. 25x2y" + 25xy' + y = 0 y(x) = ,X>0 Submit Answer

Answer 1

Here DÊ is 25 2²" +25xy + y = 0 we Se the transformation z = lna 22 dx 위상 dz Asmin, day 11 dx2 dhe 2. 1 d22 x2 dt os. da2 non put (ii) and (ii) in () 25 l d22 + 25 dy at 00 25 d²y d42 ma be a trial Det "goe (to) 25m²+1=0 Then, Somsion of (is). ausiliary egnasion. Where ind-1 be the mo al conen, Geeneral complementary solution of Ciu) is y(?) = C, cos} )4 C, sin(2/5) G, G are arbitorys constant

so, & 2 Sim Now change the independent variable x from 2, you) a e, cos ( 12) Sin 'n ,*30 Where a, are and biterys constant, this is solusion of De given by ☺ 25227" + 25xy' ty=o.