Consider the initial value problem: $$ [3) y*[\prime prime prime) -3 t (2) y*[\prime prime]+5 t y^{\prime)-6 yt*(-1), \quad y(2)=0, [\prime) (2)=1y{\prime \prime) (2)=0 $$ The real numbers $a, b5 and $c$ such that $y(t)=a t+b t*3}+c\left(35 + [2]-+*{-1} ight)$ is the exact solution of the IVP are: $a=-31 / 16, b=31 / 128, c=1 / 24$ $a=-31 / 16, b=-31 / 128, -1/ 24$ $a=31 / 16, b=-31 / 128, c=1 / 245 $a=-31 / 16, b=-31 / 128, l / 245 Consider the initial value problem: $$ **[3) y"[\prime prime prime]-3 t*[2) y^{\prime prime)+6 + y^\prime)-6 y=t":{-1}, \quad y(2)=8, C\prime] (2)=1, y^{\prime prime) (2)=0 $$ The approximation of $y*(\prime)(2.4)s by using Euler's method with $h=0.25 is most nearly: $0.94255 0,9422 $0.9423$ $0.94245 Consider the following initial value problem: $$ y{\prime)+\frac{3}t) y=1,1 \leq t \leq 2 \text { with ) y(D=1 $$ The value of $c$ such that $y=\frac[1}{4) t+\frac{c^{2}}$ is the exact solution of the IVP is: SP SD.445