Homework SourseSolve y xyy2 1Solutiony xyy2 1 or dydx xyy2 1 or y2 1y
Solve y\' = xy/y^2 + 1![Solve y\' = xy/y^2 + 1Solutiony\' = xy/(y2 + 1) or dy/dx = xy/(y2 + 1) or, [(y2 +1)/y] dy = x dx or (y +1/y) dy = x dx so that (y +1/y) dy = x dx or, y2 / 2 +](/WebImages/44/solve-y-xyy2-1solutiony-xyy2-1-or-dydx-xyy2-1-or-y2-1y-1139027-1761610436-0.webp "Solve y\' = xy/y^2 + 1Solutiony\' = xy/(y2 + 1) or dy/dx = xy/(y2 + 1) or, [(y2 +1)/y] dy = x dx or (y +1/y) dy = x dx so that (y +1/y) dy = x dx or, y2 / 2 +")
Solution
y\' = xy/(y2 + 1) or dy/dx = xy/(y2 + 1) or, [(y2 +1)/y] dy = x dx or (y +1/y) dy = x dx so that (y +1/y) dy = x dx or, y2 / 2 + ln I y I + a = x2/2 + b, where, a and b are constants, or, y2 + 2 ln I y I + c = x2 , where, c = 2(a- b) is a constant. Then x = ± ( y2 + ln I y I +c)1/2
