Question

solve the equation by method of variation of parameter?

g' ey'e ya e Solve the equation bg method of Variation of Parameter? XS REDMI NOTE 8 PRO AI QUAD CAMERA

Answer 1

Solution 7 ell Solve by Method Veuiation of by using of Parameroes, y"-ay' + y = x it's is in the General Solution form of y = yet ye homogeneous Pauticular Solution Solution find yo , "-2y'+y=0 Lit's Auxiliary Agn is (m2-2ř+1)=0 (m-1)2 =0 m=1,1 then Yc= a ² + x C₂ C² Ye= Cata (2) ex where and xez gizer the is then the whoskian of function ez xe ex co - (1+x)e? le 2g3C1+x) – xexjo W = (exy? +(@2)? x-c@mj?x (ez)? w= Now, find w and W2 - xel 10,= 25 (ta) er cezy ? W, = x4

W2= ez Some (ez -0 ez 25 we get y yi= er Ya = xer (exy2 ) 2 W.= -(0%)? 24 تركيا 25 # Yo= uigi+ Ugya where ü' = wi -2337224 1 = 24 - U,= " = (egy S - - 2 x gx U = W2 25 23 U₂ = S 1 2 si de a 323 (@232 out 5 . 4204 U2= 4004 ypa I 333 e?+ liten gecerte Z Yr = e². 323 4803 yp e ? 1273 cuinen equation the Cheneral solution the Hence ris 8 Ger+ Ca de er ter = y = yet de 1243 g ciertcaker te 1273 Solved