Please make the answer from your own work please with details I would give good feedback

6. Here is another orthogonal trajectories problem a] Draw the family ofmrres y = _+1.u'l: 23: for k :3 23:. b] Figure out the equation for its family of orthogonal trajectories. c] Draw this famy of curves on the same coordinate plane as the other family. '3". The differential equation below is not separable. {Try separating it to see for yourself] in its current state. it is impossible for the left side of the equation to be the result of a product rule. We will need to begin with a step of algebra instead. d? +32 =IE-2 xy x a] Multiply both sides of the equation by l [x]. This lnclion x) is called the integrating factor. b] We already have y and its derivative dyfdx showing within separate terms. That partis good. d? l + 3 2 I (x) a x ( (be Choose l{x) in such a way that the left side of the equation forms the result of a product rule. c] Perform the product rule backward to rewrite the left side of the equation. d] Integrate both sides of the equation with respect to x. e] Solve for y