Question

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10 1. Solve xy' = y + rey/

Answer 1

Give equation has homogeneous functions , simply put y=v/x to solve the equation.
Sol":. if olul f (x, y2 f(x, y) sane oy y . , where f, Croy) is fuction of a f farx,y) is func" of a 31 4y homogene Leous funch of ie ficx,y), f(x, y) are same degree then.. AL put y = vix . V+ du are Now, au dy cording to question. 4/20 xy = y + xe dy = y + ey/x y tini) an 2 now put را۔ = V+x.du tii) V+x.dv dx y = V. dy an -dt put (if (ii) un equ (ii) = Vte ě Lev dv ft de Jer du og į die logge + c xdu da 09 -e-v Scanned with CamScanner

again put v=y 2 /x In a + c take Natural log both side lne 9770 + Inc ylhe x tlne y = x + Inc Ang 2 es Scanned with CamScanner