(1) Classify the following differential equations as an ODE or PDE, give the order, and indicate the independent and dependent variables. If it is an ODE, determine whether it is linear or nonlinear. (a) (t2 + 1 )- dx dx +t- d+3 dt dt ( b ) dy + (+ 2 - E dy = 6 Cost at(2) Determine if a: = 2005i 35int is a solution to I\" + :r = D. (3) Determine whether y In y 2 122+] is an implicit solution to the differential equation dy = 2 1. d1: my (4) Construct a direction field for the differential equation dy dx = y - y by taking advantage of the autonomous nature. Then draw a solution curve to the initial condition y(0) = 1 and calculate lim y. 101 -10 -8 -6 -4 -2 2 4 6 8 10 2 4 10(5) Use Euler's method with h = 0.1 to approximate the solution to the initial value problem y - yz , y(1) = -1 on the interval 1