Question

Find a second solution of the given differential equation y2(x). Use reduction of order or formula. y"- 6y'+25y =0; y1=23cos(4x)

Answer 1

Y"_64'+254 = 0 1 Y=e3x cos Close by reduction of orded formula, re-S plocida y = y [D.E is y" + Plazy' +986)y=0] ere P(2L) = -6 femalos (AR) S idne CScanned with CamScanner

youre actions 320 r 60 dac Y = e cos(406) esco C) - 20% cosclos). S ces compte en cosllove). Early - cosum). Samen coS62) 32 sin (426) 4 this it while is can be admitted, since can be added to the constant, writing general solution, y=GY + 242 B 32 i. Y = € Sincl22) C Scanned with CamScanner
the 1/4 in y₂ can omitted from theses since while writing solution y(x)=c₁y₁+c₂y₂ , 1/4 can be added to constant c₂.

So y₂=e^3xsin(4x)

Here we reduction formula to find y₂.