In Problems 31-44 solve the given differential equation subject to the indicated initial condition. dy 31. xy x', y(1) = 2 dx IRST-ORDER DIFFERENTIAL EQUATIONS 32. (x2 + 2y?) dx = xy dy, y (-1) = 1 33. 2x2 -2 = 3xy + y2, y(1) = -2 dx 34. xy dx - x2 dy = yVx2 + y? dy, y(0) = 1 35. (x + ye /*)dx - xe"/* dy = 0, y(1) = 0 36. y dx + ( y cos- - x ) dy = 0, y(0) = 2 37. (y2 + 3xy) dx = (4x2 + xy) dy, y(1) = 1 38. y' dx = 2x3 dy - 2x2y dx, y(1) = V2 39. ( x + Vxy)- dy xy=x 1/2ysh, y(1 ) = 1 dx 40. y dx + x (In x - Iny - 1) dy = 0, y(1) = e 41. y' dx + (x2 + xy + y? ) dy = 0, y(0) = 1 42. (Vx + Vy) dx = x dy, y(1) = 0 dy 43. (x + Vy- - dx - = y, y(3) = 1 dy 44. _y - = cosh y(1) = 0 dx x'