question B and C, how to do it

Next consider the ODE for u[t) as a function of time: (1211 d1: 2- 2_ 3_ = _ (t 1)t alt? +2t dt +6u 0 {1) . By making the change of variable :1: = % in (1) and 110%} = y(:r(t)} you will obtain an ODE for y(:r) with derivatives with respect to the variable :12. Note that a: near zero corresponds to the long time behavior for t near 00. Using the chain rule as per below, nd the ODE that the solution of (1) satises in the variables a: Formulae: a: = %, so in the new variable 1' : du dy d3: dy l . Solve the ODE for y(a:] you found in (B) with the initial condition at a: = 0 given by yl} = 1, -] = 0. Using this solution, nd the long time behavior of the associated solution t) of (1) as t > oo