Question

This is Math Differential Equation. Please Show Your Full Work. Thank You!

8. (7 pts) Solve y"-10'+25y Se In x by variation of parameters.

Answer 1

Solve o 25= Se oae x by Variaton of Parameters iven eauatton is - we need to find the Complementar selubin first for thisfferential equatin Auxiliay eauation is m arm 25- (m-5) S Gx + C e Kesx i(x)=es 2(x)= u esK The wek Wronjkian ef these two funetion te xes elon

fun damenty We know that f y, and are Set of SoluHon fov (y x) Then a Particular soluhi to the noh homegoneau ifferential eauction is g)he (x) 2(x) eSx t re oex Put al the Valuo in eauation x) du 4x Juet 4x ) -5ex xesetxJoxd Sx

Hence general solutim of eauafim y(x) C.P P. S _sxe"lx. yo)(G+Gx)e -tx integral term can be evaduete tha^ wing geienctific calculator