Consider the initial value problem: $$ t^{3} y^{\prime \prime prime)-3 t^{2} y^{\prime \prime]+5 t y^{\prime)-6 y=t^{-1}, \quad y(2)=0, y{\prime) (2)=1, y^{\prime \prime} (2)=0 $$ The real numbers $a, b$ and $c$ such that $y(t)=a t+b t^{3}+c\left(35 t^{2}-t^{-1} ight)$ is the exact solution of the IVP are: $a=-31 / 16, b=31 / 128, cel / 24$ $a--31 / 16, b=-31 / 128, c=-1 / 24$ $a=31 / 16, b=-31 / 128, cel / 24$ $a=-31 / 16, b=-31 / 128, c=1 / 245 Consider the initial value problem: $$ t{3} y"{\prime prime \prime)-3 t^{2} y^{\prime \prime]+6 t y"{\prime)-6 y=t^{-1}, \quad y(2)=0, y^{\prime} (2)=1, y^{\prime \prime} (2)=0 $$ The approximation of $y"{\prime} (2.4)5 by using Euler's method with $h=0.2$ is most nearly: $0.9425$ 0,9422 $0.94235 $0.94245 Consider the following initial value problem: $$ y"{\prime}+\frac{3}{t} y=1,1 \leq t \leq 2 \text { with } y(1)=1 $$ The value of $c$ such that $y=\frac{1}{4) t+\frac{ct^{2}}$ is the exact solution of the IVP is: SP.SD. 445