Problem 2. (10 POINTS). REDUCTION OF ORDER, VARIATION OF PARAMETERS. Consider the following IVP: Sty-2y=3t2-1, t21,...

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Problem 2. (10 POINTS). REDUCTION OF ORDER, VARIATION OF PARAMETERS. Consider the following IVP: Sty"-2y=3t2-1, t21, y(1)=3, '(1)=0. (a) (4 points) Given that y(t) = t2 is a solution of the homogeneous ODE ty" - 2y = 0, use reduction of order to find a second linearly independent solution y2(t) of (3). (2) (3) (b) (5 points) Given y1(t) = t2 and y2(t) from part (a), use variation of parameters to find a particular solution y,(t) to the original ODE (2). (c) (1 point) Using results from parts (a) and (b), find the solution of IVP (2). Problem 2. (10 POINTS). REDUCTION OF ORDER, VARIATION OF PARAMETERS. Consider the following IVP: Sty"-2y=3t2-1, t21, y(1)=3, '(1)=0. (a) (4 points) Given that y(t) = t2 is a solution of the homogeneous ODE ty" - 2y = 0, use reduction of order to find a second linearly independent solution y2(t) of (3). (2) (3) (b) (5 points) Given y1(t) = t2 and y2(t) from part (a), use variation of parameters to find a particular solution y,(t) to the original ODE (2). (c) (1 point) Using results from parts (a) and (b), find the solution of IVP (2).