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

1. Solve the differential equations. Express 3: in terms of x in simplest forml dy_ 2 [y31' _ 23 a) [ix51y b) (ixx c) {ix43C}: 2. [n manyr differential equation problems, we need to nd a particular solution that satises an initial condition. This is known as an initialvalue problem. a) Find a solution of E = 2}? that satises the initial condition 33(0) 2 3. The notation 31(0) 2 3 means that y = 3 when x = t}. The graph passes through the point {I}. 3). b) Solve the initialvalue problem dy _ 6x2 dx_2y+cosy \"2):\" 3. For each differential equation shown below, draw a zoomedin coordinate plane with each axis showing integer values from 2 to 2. At each point represented by two integers [there should be 25 of them], draw a little line segment to indicate the slope of the direction eld at that point. Then sketch the graph of the solution to the initialvalue problem. {I d 3) i=X+y YUD=1 h) dZ=x2+y21 yapzu