dy = = x 2 ( zy dx ) + y 2 ( 2 x dy 13 ( 21-1) ( 1) ) + 1( 2(1)(1) ) - 2 2 7. Consider the differential equation - dy 3x da y where y > 0. All points in the xy-plane such that dy = 1 are in what quadrant? 1= 3X 3 - yoxax 1 1 = 13x 1:3X C 3 = X 1 = x 1 = 3 X 8. Consider the differential equation - what is the approximation of f(2)? dx dy = 2x2 + y. Using the line tangent to the curve at (1, 2) 2 x 2 dx = lydy = 2 x3 + C ( 112 ) 2 ( 2 ) + 4 2 2 = $3 + C 3 +3 3 313/ 7 C (12 ) yz - 40 4/3 = C 3 9. Consider the differential equation dy 2 2 1- 3 dx 5. Let y = f(x) be the particular solution to the liz dy/ =fi's ax differential equation with initial condition f(2) = 4. What is lim f(x) da? y = = + C ( 2 , 4 ) - y = - x - + c - 41 = - 4 + C 0 = C 10. Consider the differential equation " = cos(x). Let y = f(x) be the particular solution to the differential equation with initial condition f(0) = 8. What is f()? cosxax = / dy y= sin ( ? ) + 8 y = Sinx + C (0. 8 ) Y : - 1 + 8 ( 0 , - 1 ) 8 = sin(0)+c Y = 7 3 - C