Question

dy y-x (S1.3) Find the particular solution of wit y(17) 17 Answer: + In (578) =

Answer 1

"Dy/dx = y-x/y + x y(17) = 17 let y = vx and dy/dx = v + x dv/dx implies v + xdv/dx = vx-x/vx + x or v + xdv/dx = v-1/v + 1 implies x dv/dx = v-1/v + 1 - v or x dv/dx = (v-1) - v^2 - v/v + 1 = -1-v^2/v + 1 or v + 1/1 + v^2 dv = -1/x dx now integrate on both sides, we get integral v/1 + v^2 dv + integral 1/1 + v^2 dv = -integral 1/x dx implies 1/2integral 2v/1 + v^2 dv + integral 1/1 + v^2 dv = -ln